In the hotel fashion, might be difficult. Think of it this way, if we make the Hilbert Hotel infinitely tall and each floor has infinitely many rooms such that they correspond to each rational number, we can fill any number of people from any source on the first floor alone.

I think we could only do this with an even more absurd scenario like if each room was filled with pregnant women who are giving birth, and the children rapidly age, and also give birth at an infinite rate? That would create an infinite nesting doll like situation for each guest