I don't know if this is often done, but I am wondering about changing the size of my rear wheel, but not sure how much work is involved. I was thinking of something around the same as the fatboy rear wheel, to me a softail frame is used, or is there more to it than meets the eye. I have a 2013 FLSTC, and I love the bike, and the only thing I feel lets it down is the size of the rear wheel, or maybe put a larger rear tyre on the bike, how much bigger can I go with the tyre, any ideas.
Search function on this site will be helpful to you, as its been done before, think Harley sells a kit if your feeling rich, as it won't be cheap to buy it from them. Check the online catalogues for the price and parts needed. Sometimes its cheaper to buy the bike you want than to start buying and swapping parts on the one you have, especially if someone else is being paid for the labour.
Alloy Fatboy wheels are a good choice as Harley chrome rims and spokes rust and may not by trued very well.
Assuming bigger means wider, personally I wouldn't go wider than 170 or max 180 mm rear or the bike wants to stand up going around corners. If it gets any wider bumps and dips also have a greater influence on the bike, tipping it left or right as the road/tyre contact point is getting too far out to the side from the bikes centerline and are not absorbed by the bikes suspension as they should be. Another thing is the primary drive stops you from moving the belt across to keep a wide rear tyre on the centre line of the bike, consequently the wheel gets moved out to the right instead (come from the factory like that) which also does not do the handling any favours. Thats why the 200 mm rear tyre models have a narrower belt and the wheels shifted out to the right, it is a bandaid fix, but cheaper than trying to remake the engine/clutch/gearbox mechanicals fit properly. Often see second hand swingarms off 200 mm rears on gumtree for a low price, not sure why they are taking them off, for chromed or even wider ones maybe? Haven't swapped a wider one on myself as mine was already a 200 mm rear, I ended up putting a narrower rear rim on mine to get the bike handling better and also get the rear wheel back closer to the bikes centre line instead of being out to the right hand side. Its much better now, might not look as cool, but handles significantly better. Kept a 200 mm rear wheel to put back on the bike if I sell it as most people would rather the cool look than fun and safety. I put it back on occasionally to remind myself what it was like or to waste a bit of rubber because thats all it is good for. Tried putting wide tyres on a narrow rim when I was young and stupid and bullet proof, won't do that again. Would rather come out of a corner with a smile and looking for the next corner than white nuckles from scaring myself by trying to do the corners at the same speed, can still remember which corner it was. If you just putter around below the speed limit the above may be irrelevant. Hope I haven't wasted 5 minutes of your time and its some help.