Sure, you can connect multiple things by stacking tee fittings.
There are two things to be aware of with the specific arrangement you're considering. One is that 3/8" hose is terribly small for a [clothes] washing machine. You'll do better to remove the angle stop valve, which sits on 1/2" pipe, and insert a tee there with a 1/2" valve just to serve the clothes washer.
The other thing to be aware of is that if more than one thing demands hot water at the same time the flow to all the things will be low. The 1/2" supply pipe is just too small to serve concurrent loads. If you can deal with the reduced flow, or simply coordinate the uses to avoid concurrency, it'll be fine.