What works is observing how your son reacts to the routine, not the number of activities themselves. If he's happy, sleeping well, not complaining about being tired, and his grades aren't dropping, he's probably fine. But if you see him stressed, irritable, sleeping poorly, or constantly asking for breaks, that's where the limit is. Every kid is different; some enjoy staying busy and others get overwhelmed easily.
What I'd do is ask him directly how he feels about all this. At 10 years old, they can already express whether they feel pressured or if they're actually enjoying it. If he wants swimming because he genuinely likes it, maybe he can do it. But if it's going to be because you think he "should be doing several things," better not. The point is that activities should be for enjoyment, not obligation. If he has to choose, fine, but let it be his decision.
Also factor in quality family time and rest. Homework plus three sports plus piano is quite a lot for someone his age. I'd say two extracurricular activities plus one artistic one (like piano) is a good balance. If he really wants swimming, maybe he could skip one day of soccer instead, so he's not adding but reorganizing. But observe him for a while; sometimes kids ask for things because their friends do them and then lose interest quickly.