I’ve heard that Google likes sites with lots of pages. Is this true?

In one word, no. Every page at Google is ranked by itself, not as part of a collection of multiple pages from a single site. It may be that the spidering of a site for inclusion into the index involves heuristics that depend in part on the number of pages already found on the site, but I have not seen such an effect.

That said, the goal is to have lots of pages to use to build PageRank and Link Reputation.  You can have those pages on one site, or on several. It does not matter, so long as you build the pages.