Since some spells say that you can summon several several creatures at once and not all summon spells require concentration there schould be no limit of having only 1 summon at a time.
So yes, a wizard should be able to have a familiar, animate dead and one other conjuration spell active at a time.

That being said I agree with Stabby: Its too early to know things for sure.
- Max lv is 4, so we cannot have animate dead at the moment, or any other spell with several summons.
- The necromancer subclass is not implemented yet and it would be pointless because we cannot get animate dead anyway.
- Animate dead is the only spell that lets us summon undead. You only summon weak zombies or skelletons and it is considered evil so every non evil NPC (and maybe some evil ones too) would attack you if you go to town with a zombie army.
- The concentration mechanic was added to prevent things like your kingmaker screenshot and endless pre buffing. Some people may not like it, but thats a fundamental rule of 5E.

groovy Prof. Dr. Dr. Mad S. Tist groovy

World leading expert of artificial stupidity.
Because there are too many people who work on artificial intelligence already :hihi: