It's possible to get 7-10 days worth of stuff if you're not concerned with wearing pretty much the same clothes for that time. Obvious: wear the heaviest pair of shoes on flight, plus the bulkiest sweater, coat in the overhead.
As pointed out, hotel laundry is available, or hand wash essential items overnight. We often rent a flat and washer/dryer is a wonderful asset, but you can still manage without one.
Put toiletries in small bottles, use space-saver bags, and - most important - resist the impulse to throw in yet another extra sweater.
I use a 20' rollaboard plus a smallish backpack which does double duty as a footrest, or increases the height of one when I'm in J. It's well worth it when you bypass the crowds at the baggage carousel.