Is there a way to get more than the original ten pets?

Yep! You can buy up to 25 slots in the Millionaire Center starting at 20m sP apiece (the first 10 slots increase in price by 20m at a time, so the 10th costs 200m and then the 11th goes back down to 20m again. I believe the same would happen after the 20th, but I actually missed at least one of those slot additions happening somehow, so I'm not positive) You can also buy up to 65 additional slots for 1500 CSC apiece through the Pets page You can also unlock one pet slot from the Loyalty Box you get starting on your second anniversary of joining the site, and sometimes they're given out as prizes from events like Quest-a-Thons.