Here are two public-law constraints to meet.
1. ERISA § 404(b) [29 U.S.C. § 1104(b)] commands “maintain[ing] the indicia of ownership of any assets of a plan [within] the jurisdiction of the district courts of the United States.”
A rule allows holding securities through intermediaries if enough control is with a sufficiently regulated and capitalized U.S. bank, insurance company, or investment adviser.
29 C.F.R. § 2550.404b-1 https://ecfr.federalregister.gov/current/title-29/subtitle-B/chapter-XXV/subchapter-F/part-2550/section-2550.404b-1
It is common for a U.S. bank or trust company to use non-U.S. subcustodians, depositories, and clearing agencies.
2. Under the Internal Revenue Code of 1986, a tax-qualification condition calls for a domestic trust.
A trust, including a § 401(a) retirement plan’s trust, can be a “United States person” trust if (i) a U.S. court can exercise primary supervision over the trust’s administration; and (ii) a United States person has authority to control all substantial decisions of the trust.
26 C.F.R. § 301.7701-7 https://ecfr.federalregister.gov/current/title-26/chapter-I/subchapter-F/part-301/subpart-ECFRbb5a653881cc2c0/section-301.7701-7
It’s feasible to meet that rule without undoing a participant’s power to direct investment, even if the participant is not a United States person.
If the plan’s governing documents would provide that “each Doctor is Trustee for her/his account”, the plan’s sponsor and fiduciaries might adjust those provisions regarding a participant who is not a United States person.