I know that characters with at least one level of Artificer get an Iron Defender (that has a level of Fighter for every level of Artificer its owner does), characters with at least one level of Druid get a Wolf Companion (that has as many levels of Ranger as its owner does Druid levels), and Wizards that get the Skeletal Knight enhancement in the Pale Rider enhancement tree get to summon one that is like the odd one out compared to the other two class pets (no character sheet, and it's upgraded with further enhancements to that tree, but it does have a level of Fighter for every level its master has in Wizard, as well as Epic levels, which may also apply to the other two).
Would it be possible to have access to all three of those pets if one were to multiclass into all three of those? I'm not saying that it would necessarily be a good idea. I just wonder if it could be done. If so, then would multiple pets be available at once? Or would the PC have to alternate between the three? Because I think it sounds cool to have three pets at once, but I know that, in practice and the context of a video game, it could get hard to manage three pets, all with their own command bar.