Controlled Group - Transfer Loan from Plan A to Plan B to follow employee from Company A to Company B

[SRM]

Consider a controlled group of companies A, B, C, D, E and F.

Each company has a separate 401(k) plan (no HCE in any plan) and separate investment providers for each plan.

If an employee of company A transfers to company B, can the employee's loan in Plan A be transferred to Plan B (trustee to trustee transfer not a rollover or distribution) if the employee's remaining balance remains in Plan A?

Clearly the plan documents, loan programs, and promissory notes would have to contain appropriate language and plan sponsors or trustees would have to accept the tranfers, but is this possible under regulations and code?