I have a 10, 8,7,7, 3yo. In our current house that we’ve been in for year now, we have a fully finished basement. It’s helped tremendously to spread out the clutter.
When we were in our small house we really were vigilant to pair down the toys seasonally. We also were vocal about gifting our kids: clothing, books or an experience. We also had an arts/crafts/writing/school table in what would have been the dining room and held all those little pieces in plastic drawers that we could wheel around. We only had room for our play kitchen in the living, large toy box and an IKEA shelf for our puzzles, games and lego/magna tiles. All soft toys could stay in their bedrooms.
Truthfully we have books, dress up clothing, play kitchen and market, lego, magnatiles, arts and crafts, puzzles and board games. We keep the outside toys in a toy bin in our garage.