The KDF9 (English Electric, 1963) had a hardware option for timesharing. This provided four instances of most per-program context: the nest (16-deep expression evaluation stack), the subroutine jump nest (16-deep return address stack), and the 16 Q-stores (modifier/counter registers).
The timesharing director (=operating system kernel) therefore supported up to 4, no more, concurrently executing programs. Context switching avoided the need to save and restore 48 registers. So, context switching was relatively cheap for such a sophisticated machine (unless you were paying to buy the hardware). Each of the 4 possible programs had an associated priority, and completion of I/O by the hardware was cognizant of whether the completed I/O belonged to a higher priority level than the currently-executing program.
I don't think I've ever heard of any other system that provided this level of timesharing support in hardware. The ICL 1900 system sort-of comes close, in that the resident exec had a small and fixed limit on multiprogramming, but I think that's due to exec storage limits (tables take space).
These days, of course, 4 processes is indistinguishable from zero, but 4 wasn't necessarily a huge barrier in the 1960s (KDF9 had 32Kwords memory, max, so you're not fitting too much in there).
Anyway: what other systems had hardware per-program resource replication?
(Apologies for another list-oriented question, but quite frankly, the discussions that ensue from such forms is more interesting than the "here's a question, here's the answer" format. It's in the nature of historical information that people know different corners of the subject.)
Wikipedia's page on the Ferranti Orion lists a handful of computers, including the Orion, that had 'hardware support for timesharing', but it's not clear to me whether that included replicated hardware. Maybe there was nothing to replicate -- the Orion accumulators were just the first 64 words of (relocated per program) address space. The minimal requirement for hardware-assistend timesharing support may be limited to provision of datum/limit registers.