The summon limit feels genuinely weird when concentration or going MAD is limit enough.
In theory you could go 3 War, 3 Ran, and 3 Art to get three "permanent" summons. But that's at the cost of 9 levels, and the effectiveness of each class is lowered so if someone wants to have more than one from different sources, I say let them.
Furthermore, mage hand should not require concentration and should not break concentration on spells. As far as I know, that is gimping the spell badly.
Concentration is the main limiter for summoner's, and that's why conjurer's get a level 14 feature to not have it broken by damage for Conjuration spells only. By getting hit the caster runs the chance of losing it or having the summon go berserk. You could waste a spell slot by summoning a fey only to have it disappear in the same round. Which is why a warlock summoner would fall back on their familiar (post Tasha's) and part of why concentration summons shouldn't even interact with permanent summons.
Which doesn't even get into my issue that familiars by raw, and mage hand, shouldn't be attacking directly like they are now. Warlocks can use their action and bonus action (Tasha's) to make theirs attack, but now all of them being able to attack creates a weird balance thing. And devalues concentration summons cause your current ones can attack and the concentration will dismiss it so just use the bird familiar to blind everything.