when i played on my old copy of the game in 2014 i used to get heaps of streetpasses, which really helped me expand my catalogue (especially because I was in the city a lot and found lots of people whose houses were a lot more complete than mine!)
i got a new console & game a month or so ago, and these days i've really been struggling to expand my catalogue. i've only got like 5 streetpasses since i started, and even though i have TIY most of the stuff is the same all the time. aside from buying stuff off people here (which i've done a bit) and doing chores for villagers, how else can i find more furniture?
Be on the lookout for catalog towns where people have items on the ground. You pick up the item and it is logged in your catalog and then you drop the item so others can do the same.
Having a second town that gets different items can really help too!
Cataloging as HHoney said, as well as checking out the Re-tail subforum here on TBT for any items you missed will go a long way for getting all those rare items. And then common items will just accumulate naturally. I don't think it'll be a big deal