Hilbert’s Grand Hotel can manage an infinite number of boulders, each containing an infinite number of Sisyphuses (Sisyphi? Sisyphes? Sisyphodes?) by designating each boulder a prime number and each Sisyphus a counting number, and multiplying the two to get their room number.

This leaves some rooms open for additional guests, which may get management angry about underutilized rooms. There are other configurations that pack everyone in more tightly.