I live in an Upstairs apt with just one. She will not go downstairs , which is good. And I carry her leash, harness and all every time. I could not imangine three of them.
I think A Condo, or townhouse would be a lot more suitable for you with three yorkies, and possibiliy more accomodating.
LIving downstairs is the best thing to do as well too. And having access to a back door or to go into will help you manage all three dogs at once.