@Madscientist3 mentioned the melee sorc build as an exception in one of the previous posts. But, there are definitely some exceptions.
The main reason, I find is to add some mobility or versatility to companions specifically. If you want to get a different mount for Seelah, for instance. You could take a Beastrider level before you get divine bond to get your pick of any animal and you wont lose any BAB or mount progression. You do however, lose your capstone ability and a tiny bit of spell progression (not a big deal for paladin anyway)
Some things that you have to watch out for are drops in BAB by taking dips in 1/2 or 3/4 BAB classes. This isn’t really an issue for fighters, cavaliers and other full BAB classes.
On the caster end, is drops in caster level. While the Melee Sorc is fun, you do lose 3 caster levels and it drops your spell progression a good bit initially. Especially, now that they’ve broken the merged book progression (Hopefully that gets reverted back to what it was). It wouldn’t be as good as it is without the merged book.
You lose your capstone abilities, which in some cases are great. Like a rogue’s master strike, is pretty sick, for instance. But, if the capstone can be replaced by a spell (Immunities) than it’s not really a big loss.
Some examples of companions that I like to Multiclass are Regil and Lann. For Regil, I love taking one level of divine hunter (hunter) to give him a velociraptor, lead blades and acid maw(albeit for one minute). Then going Gendarme (Cavalier) to keep giving him lots of feats for himself and his raptor. He gets an insane amount of attacks, outflank + leading strikes+ ever ready all work off of eachother. And, he can get full attacks off each round. He went from someone that I never had a use for in alpha, to someone that I almost always take with me.
For Lann, I like to do Zen Archer 3/Demonslayer Ranger 17 with a Mastodon pet. Why use a pet on a ranged character? You can give him shortbows and the limited range doesn’t become a problem for him since his mount can move him wherever he needs to be. Another benefit is that you can take the full snapshot line and use outflank and ever ready on an archer. This combined with the Mastodon’s overrun ability is just great. You can open up combat by charging into the groups of enemies with Lann, tripping everything he passes by and he gets AoO’s when they try to get up. It’s lots of fun. He doesn’t lose any BAB, and gains a ton of versatility that he wouldn’t normally have. +8 favored enemy bonus to all demons is great for an archer too.
A lot will also depend on what difficulty you are playing on. As Hard, and Unfair, really punish you for not maxing out your BAB. And you need to have fairly optimized builds if you don’t want to end up pulling your hair out. It depends on what you want to do with said character too. If you can find an archetype that has everything you want, might as well stick with that. If you’re stuck with a partially premade companion. There are certainly different avenues that you can explore, as shown above.