R.J.
My rule of thumb is WHENEVER we start making excuses to stay home, or we feel like we're missing out on something else, it's time to drop something.
Interestingly enough, it's not always (or even usually) the activity that gets missed that is the "one too much", but rather another (lesser liked/loved) activity that sets us up for being tired/wanting to stay at home during a beloved activity.
We homeschool... so we do WAY more activities than most people (so using our schedule for comparison undoubtedly would look ridiculous), because we have an extra 8-10 hours in every single day. Our year round schedule has art, music, gymnastics, aikido, breakdance, and swimming every week (in addition to school work, and seminars, and field trips). Then we also do 1 seasonal sport every season (soccer, snowboarding, baseball, and swimming). On top of those, we have "school break" camps (aka the camps that are offered during public school breaks). We've been trying to work in chess & drama & boyscouts & lacrosse & basketball for 2 years, but none have worked schedule wise. (Drama, instead we do as camps... but chess and boyscouts we'd REALLY like to do, but just haven't figured out the time for it).
See? Sounds nuts, I'm sure. For US, however, it's a relaxing schedule. Kiddo is out of the house in classes or sports taught by another adult between 1-3 hours a day. We spend about $150 a month on those classes in total, so there's no financial stress either. Public/Private school families though, have to figure out ways to do activities AFTER having their kids be gone for 8+ hours a day (I say 8-10, because of drive time and many who are in daycare until 5pm), AND get HW done, AND have family time. Which at least, is what we had to do when kiddo was in away-school. We could MAYBE do 1 outside activity instead of 7 (not including camps and seminars). And we'd REALLY like to be doing 12, but as I said.. right now those extra 5 just don't "fit".