I missed out on all the stuff between 7 speed freewheels and 11 speed cassettes. But just be wary that what you get is compatible with the freehub you have on your bike. I suppose you are back in the days where you can build your own stack so maybe you just need to replace a cog or two if you can find them.
If your DR can't handle the physical clearing of the bigger cogs you choose, then you can put a hangar extender on it. But that doesn't change any of the front difference or total capacity specs. Though you can always try and see if you can go a tooth or so more. Maybe maybe not. Bikes are different.
If you decide to spend money on a crank, I'd very much recommend you also consider a 2 piece crankset and BB that will move the BB bearings further outboard. Not so much that you'll notice the difference while on the bike, but you'll open up availability to more crankset choices whether you actually get one or not.
And rear DR's in the Shimano 105 line and below tend to be very inexpensive when new. Though depending on what you get you might have to change shifters, and that can be pricey.