VM/370 was a descendent of CP/67.
VM/370 provided virtual machines equipped with virtual memory.
Someone from IBM observed that when VM/370 ran as a guest of VM/370, two copies of the same cache algorithm were running, one atop the other, each oblivious to the other.
Each uses its ‘real’ memory to cache pages of its gueses with the ‘real’ disk as the backing store.
If the virtual real memory (SIC) was larger than the real memory—a common situation—then the effective page replacement algorithm for a guest of the guest was pessimal assuming that both algorithms used perfect LRU.
This fails to be analogous to modern multi level caches in that only the memory mapping function is composed in the stacked virtual machines, whereas data is actually moved and brought closer to the CPU in stacked caches.