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assuming you pay for feed and lodging regularly, given enough time using Handle Animal, you could keep a large retinue of trained animals.
what's to stop you from bringing your dog pack adventuring?
I am the DM of the group and want one of my goblin NPCs to command a gang of goblin dogs. but i also know that if i do this, it'll give my PCs ideas, so, i want to be ready for both situations with a decent rules-grasp of the situation.
How about you can attempt to command a number of HD worth of animals equal to your Handle Animal bonus at one time, however, only one additional creature (beyond the first) actually follows your orders per 2 you beat the command's DC by?

Azoriel |

What's to stop your players from doing the same with a bunch of NPC hirelings?
It's not difficult to produce a mob of NPCs for support so long as you have the resources to gather and (maybe) maintain them. It's usually not a good investment though, since they tend not to gain levels at the same rate the PCs do.
It's very easy for the DM to produce a bunch of trained dogs, because the weeks or even months it took to accrue that many trained dogs was something that happened off-screen, and the personal investment the DM puts into the matter is pretty much nothing beyond simply saying, "This happened." As such, when the PCs wipe the floor with said dogs, it doesn't really matter to the DM. (The dogs moreorless served the purpose they were intended to - provide a challenge to your players and die.)
It's another story for the PCs to gather a bunch of trained dogs, whether through monetary investment or taking the weeks/months needed to train them. Each dog death is a permanent loss of capital (time and/or money) that the PCs labored towards producing each dog. This is in no way the same thing as you waving your hand and saying, "So there's dogs there now, okay?!?" PCs going down this road will eventually be left with sagging empty coinpurses, a bunch of dead dogs, and (if they are at all wise) regret over the fact that they didn't put their money towards gear for themselves like they should have.

Azoriel |

As for the original question...
does the DC (or action) increase to give multiple animals (of the same type) the same command?
is there an upper limit? (for example dog-walkers IRL usually top out at 8).
should this be moved to homebrew?
Rather than complicating things, I would restrict usage on how the commands are being given.
If the dogs have been trained to attack off of verbal commands, and especially if the trainer has been working towards them being able to receive attack commands as a pack (which may or may not warrant a trick), it should really only take a single command to have all the dogs attack. (Bear in mind the dogs probably aren't going to go after specific people in this case, but instead just go after the nearest individuals in the group their attacking.)
This would just be one action on the part of the person directing the dogs. The difficulty of the handle animal check wouldn't be any higher than just directing a single dog. This would be analogous to someone directing a bunch of wardogs, or setting a bunch of hounds loose to hunt an animal. (I don't imagine the houndsmen in those cases needed to be particularly skilled to deliver those commands.)
If you had any other means of direction, like reins or a leash, then I'd restrict it to one animal per action. (No particular reason for this restriction in the books, just how I would rationalize things.)