ORDER
KAREN WELLS ROBY, United States Magistrate Judge.Before the Court is a Motion to Compel Deposition Before Magistrate Judge Roby (R. Doc. 1107) filed by Laurin Maritime (America) Inc., Laurin Maritime AB, White-fin Shipping Co., Ltd., and Anglo-Atlantic Steamship Limited seeking an Order requiring D.R.D. Towing Company LLC’s witnesses (“DRD”), Julie Dantin Schmidt and Randall Dantin, to appear for a second deposition before the undersigned so that the Court may determine whether the witnesses can properly invoke their Fifth Amendment rights during the course of the deposition. On March 22, 2011, DRD filed a response. (R. Doc. 1114.) This motion was heard with oral argument on Wednesday, December March 30, 2011.
I. Background
On July 24, 2008, Plaintiffs Stephen Marshall Gabariek and Bernard Attridge filed this class action Complaint. (R. Doc. 1, p. 1.) On August 6, 2008, the case was consolidated with several other cases resulting from the same underlying incident.1 (See R. Doc. 10). *210On July 23, 2008, the M/V Tintomara, a tanker, collided into Barge DM932 while traveling near Mile Marker 97 of the Mississippi River near the Crescent City Connection. (R. Doc. 1, ¶¶ 1, 5.) The barge was towed by the M/V Mel Oliver. Id. As a result of the collision, Barge DM932 split in half, causing a spill of 500,000 gallons of No. 6 Heavy Fuel oil which had recently been loaded on the barge at the St. W. Stone Oil Distributer located in Gretna, Louisiana. Id. As a result of the spilled oil, the Plaintiffs allege that serious and dangerous environmental contamination of the Mississippi River occurred, and an 80 mile stretch of the Mississippi River has been closed to navigation. Plaintiffs also complain that prevailing winds have caused toxic gases from the oil to spread from the site of the collision to the French Quarter and the Uptown Area of New Orleans, exposing class members. Class members also complain that lost revenues have resulted from the closure of portions of the Mississippi River caused from the oil spill. Class members further complain that water intakes for Algiers, Gretna, St. Bernard Parish, and Plaquemines Parish have closed in order to prevent contamination to drinking water. (R. Doc. 1, ¶¶ 10-13.)
The M/V Mel Oliver was operated by DRD Towing, Inc. (“DRD”) and was owned by American Commercial Lines, LLC (“ACL”). ACL contends that DRD operated the tug pursuant to a bareboat charter agreement. However, the Tintomara Interests contests whether a true bareboat charter agreement existed between DRD and ACL.
DRD, one of several entities held under the Dantin Holding Group, was operated by three (3) principals. Randall Dantin (“Dan-tin”) served as DRD’s operating manager. Julie Dantin Schmidt (“Schmidt”) served as the bookkeeper, and Danny Dantin serves as the President. After the accident, DRD pled guilty to utilizing unlicensed personnel in violation of the Waterways Safety Act. Dan-tin pled guilty to obstruction of justice for destroying DRD’s electronic and bookkeeping information. It is unknown whether Schmidt has been questioned by the authorities or received a target letter for any involvement she may have had in DRD’s or Dantin’s wrongdoings.
As to the instant motion, on February 15, 2011, the Tintomara Interests deposed Schmidt and on February 17, 2011, they deposed Dantin2. In response to almost every question posed, including basic background questions, both witnesses refused to respond and instead pled the Fifth Amendment privilege. The Tintomara Interests contend that the Privilege was improperly invoked as to several of the questions posed and the witnesses’ failure to respond to non-incriminating questions warrants a second deposition of both witnesses. The Tintomara Interests further seek to re-depose the two witnesses before the undersigned so that any claim of Fifth Amendment privilege can be promptly resolved.
DRD filed a response, indicating that its counsel does not serve as criminal counsel for either deponent. However, if the Court were to find that a blanket invocation of the Privilege was improper, it would not oppose their redeposition so long as each deponent is permitted to have criminal counsel present.
II. Standard of Review
Under Federal Rule of Civil Procedure 26(d),“[ujnless, on motion, the court orders otherwise for the parties’ and witnesses’ convenience and in the interests of justice: (A) methods of discovery may be used in any sequence; and (B) discovery by one party does not require any other party to delay its discovery.” Fed.R.Civ.P. 26(d). The principal effect of Rule 26(d) is “to eliminate any fixed priority in the sequence of discovery.” Advisory Committee’s Note to Fed.R.Civ.P. 26(d), 1970 Amendments. A court has discretion to vary the usual priority, however, such relief is granted “only for ‘the most *211obviously compelling reasons.”’ Advisory Committee’s Notes to Fed.R.Civ.P. 26(d), 1970 Amendments (quoting 2A Barron & Holtzoff, Federal Practice and Procedure 44-47 (Wright ed.1961)).
III. Analysis
The Tintomara Interests contend that both deponents improperly asserted a blanket Fifth Amendment Privilege to the questions posed during their depositions. The Tintomara Interests contend that, although the deponents may have a legitimate Fifth Amendment Privilege as to questions which run the risk of self-incrimination, the questions asked of the deponents during their depositions did not bear such risk. The Tintomara Interests contend that he following broad categories of topics, in which it seeks to depose the witnesses, do not invoke the privilege: (1) general background information; (2) contract negotiations between DRD and ACL; (3) each entity’s performance under the contract, including insurance, maintenance repairs, and financing; (4) DRD’s relationship with other entities held under the Dantin Holding Group; and (5) ACL’s knowledge of DRD’s actions under the contract.
The Tintomara Interests contend that the deponents failure to respond to questions which do not implicate the Fifth Amendment Privilege necessitates a second deposition of each witness. They further request that the deponents be redeposed before the undersigned so that a prompt judicial resolution may be obtained if issues relating to the Fifth Amendment Privilege should arise.
DRD’s counsel does not serve as criminal counsel for either deponent. However, DRD’s counsel insists that both deponents have a legitimate privilege to at least some questions and therefore requests that if the deponents are re-deposed, they be permitted to have criminal counsel present.3
“A blanket refusal to answer questions at depositions on the grounds that they are privileged is an improper invocation of the Fifth Amendment.” Securities and Exchange Commission v. First Financial Group of Texas, Inc., 659 F.2d 660, 668 (5th Cir.1981) (quoting Note, Plaintiff as Deponent: Invoking the Fifth Amendment, 48 U.Chi.L.Rev. 158, 164 (1981)). “Even if the danger of self-incrimination is great, [the party’s] remedy is not to voice a blanket refusal to produce his records or testify. Instead, he must present himself with his records for questioning, and as to each question and each record elect to raise or not to raise the defense.” Id. quoting United States v. Roundtree, 420 F.2d 845, 852 (5th Cir.1969)(footnote omitted).
Whether a party is entitled to invoke the Fifth Amendment is not a determination for the party, and instead is a question for the Court after conducting “a particularized inquiry, deciding, in connection with each specific area that the questioning party seeks to explore, whether or not the privilege is well-founded.” United States v. Melchor Moreno, 536 F.2d 1042, 1049 (5th Cir.1976). Even where a party has a legitimate claim of privilege with respect to certain questions or lines of inquiry, that person may not be entitled to invoke his privilege to remain totally silent. Only where the court finds that a witness could “legitimately refuse to answer essentially all relevant questions,” United States v. Gomez-Rojas, 507 F.2d 1213, 1220 (5th Cir.1975), because of the threat of incrimination from any relevant questioning is a person totally excused from responding to relevant inquiries. Otherwise, a person is entitled to invoke the privilege “(o)nly as to genuinely threatening questions .... ” United States v. Melchor Moreno, 536 F.2d 1042, 1049 (5th Cir.1976). See generally United States v. Goodwin, 625 F.2d 693, 700-01 (5th Cir.1980). Therefore, a blanket invocation of the fifth amendment privilege is insufficient to relieve a witness of the responsibility to answer questions posed during discovery and to claim the privilege with respect to each inquiry. See National Life Insurance Co. v. Hartford Accident & Indemnity Co., 615 F.2d 595, 598-600 (3d *212Cir.1980); See also In re Folding Carton Antitrust Litigation, 609 F.2d 867, 873 (7th Cir.1979) (per curiam).
It is clear that both witness’ blanket assertion of the Fifth Amendment Privilege was improper. Both witnesses cited the Privilege to questions which could not remotely be construed as running the risk of self-incrimination. In fact, the only questions in which Dantin did not plead the Fifth was in response to questions asking his name, address, and birthday. (See R. Doc. 1107-3, p. 6.) Schmidt, on the other hand, indicated that she “take[s] the Fifth on everything ... Can I just say that, or do I have to say it every time?” (R. Doc. 1107-6, p. 7.) She then proceeded to respond “Taking the Fifth” to each and every question posed, including “How far did you get in school?”, “How are you presently employed?”, and “What was the first job you had out of school?” (R. Doc. 1107-6, pp. 8-9.)
As a result, the Court finds that a second deposition of each witness is warranted. Further, the Court will permit the Tintomara Interests to redepose the witnesses before the undersigned in order to provide a prompt resolution if either deponent asserts the Privilege in response to the Tintomara Interests questioning. The Court makes no determination at this time as to whether the broad topics proposed by DRD invoke the Fifth Amendment Privilege and instead will make its determination on a question by question basis. Both deponents are permitted to have criminal counsel present.
Further, because both witnesses failed to respond to questions which could not reasonably require the invocation of the Fifth Amendment Privilege, Schmidt and Dantin shall bear the costs of conducting their respective deposition.
IV. Conclusion
Accordingly,
IT IS ORDERED that the Motion to Compel Deposition Before Magistrate Judge Roby (R. Doc. 1107) is hereby GRANTED.
IT IS FURTHER ORDERED that Julie Dantin Schmidt and Randall Dantin shall be deposed United States Magistrate Judge’s Courtroom located at 500 Poydras Street, Room B-431, New Orleans, Louisiana on Friday, May 13, 2011, beginning at 10:00 A.M.
IT IS FURTHER ORDERED that Julie Dantin Schmidt and Randall Dantin shall bear the costs of their respective depositions.
. The instant case was consolidated with the following cases: Civil Action No. 08-4012, Austin Sicard, et al. v. Laurin Maritime (America) Inc., et al., Civil Action No. 08-4023, Whitefin Shipping Co. Limited, as owner of the M/V Tintomara, petitioning for Exoneration from or Limitation of Liability, Civil Action 08-4025, George C. McGee et al. v. Laurin Maritime (America) Inc., et al, Civil Action 08-4031, Bernadette Glover v. Laurin Maritime (American) Inc., et al, Civil Action No. 08-4046, American Commercial Lines, LLC as owner of Barge DM-932, Praying for Exoneration from or Limitation of Liability, Civil Action No. 08-4055, Jefferson Magee et at v. Ameri*210can Commercial Lines, Inc., et al, Civil Action 08-4058, James Roussell et al v. Laurin Maritime (America) Inc., et al, Civil Action No. 08-4059, James Joseph v. Laurin maritime (America) Inc., et al, and Civil Action 08-4050, Vincent Grillo et al v. American Commercial Lines, Inc., et al.
. At the time of Dantin’s deposition, he had pled guilty but had not surrendered himself to begin serving his 19 month sentence.
. Counsel for the Tintomara Interests represented during the hearing that Chip Forey, Schmidt's criminal defense attorney, does not oppose a second deposition. However, he does not waive Schmidt’s Fifth Amendment Privilege. DRD informed the Court that while Dantin was previously represented by counsel in his criminal matters, he is no longer represented.