Are there some plans for which no 3(16) service is available?

Imagine an employer believes it can’t or won’t, even with a nondiscretionary service provider’s help, administer an individual-account (defined-contribution) retirement plan. The employer prefers to engage a discretionary 3(16) service provider for as many responsibilities as it will take.

Are there some kinds of plans for which, considering size or some other fact or circumstance, a 3(16) provider won’t offer its services?