I backpacked through Europe 2 years ago (late August to November) and made it through with one bag. In fact, I even brought home a long wool-blend coat from H&M. And 5 or 6 pairs of shoes.
Here are 3 tips to maximize your bag:
1) Bring only what you NEED...or when in doubt, bring things you don't mind parting with
Sounds simple enough right? The time of year I went was tricky, the weather was HOT at the beginning of the trip (especially in NYC and Greece), but by the time I was going home, it was freezing in Switzerland, France and London. If you're like me and traveling over multiple seasons, it's much harder to pack.
Single season travel is so much easier: sandals, skirts, dresses, bikinis - all things you will use often. But on my trip, I didn't need that 3rd bathing suit after Greece, or the shorts. Lucky for me, I had brought some older shorts and swimsuits, so I just left them at the hostel, or you can always find a consignment store/charity shop.
2) Take the time to pack your bag
Yeah, packing sucks. Big time. But if you're trying to cram your bag with more than it should hold, make sure you take the time to pack well. I stayed at a B&B in Marseilles before going back to London so I had plenty of time to pack, unpack and re-pack my bag. I had a separate plastic bag of things that had never seen the inside of my backpack. But I fit everything in. Wool coat and all.
3) Roll & Stuff
Make use of every bit of space that you can, especially if you're short on space. Roll your clothes up to make them as compact as possible, stuff underwear and socks into shoes, whatever it takes. The packing compartments and cubes that are available are helpful, but if you can't afford those, then extra-large Ziploc bags work just as well, if not better. These items help you stay organized, and make packing simpler and less stressful. Ziploc bags are really good because you can take the air out of them, literally taking advantage of all the space you have