There's a creative way to do this using existing mechanics, however the Animate Dead spell requires you get the statistics from the DM anyways.
The restriction on animate dead limits the spell to a medium or small humanoid corpse/pile of bones. This prevents you from animating say, an Ogre Zombie (which is large size).
However, there is a handy spell you can use that will change a creature or objects size category.
PHB pg. 237; Enlarge/Reduce
Reduce. The target’s size is halved in all dimensions,
and its weight is reduced to one-eighth of normal. This
reduction decreases its size by one category—from
Medium to Small, for example.
Once you've shrunk a target from Large to Medium, Animate Dead will work on them.
Animate Dead takes 1 minute to cast (Which requires Concentration for the casting duration).
Enlarge/Reduce only lasts for 1 minute (Concentration).
You are going to need two other casters with Enlarge/Reduce to help you with this as they are going to need to take over maintaining concentration on Enlarge/Reduce before you finish Animate Dead. We already know from the rules that spells with the same effect don't stack, however their durations overlap.
So here's an example scenario:
- Caster One targets dead Ogre with Enlarge/Reduce spell and reduces it's size to medium.
- You begin to cast Animate Dead.
- Caster Two, halfway through the cast, uses Enlarge/Reduce on the dead Ogre. The spell effect is duplicated (so it doesn't stack), but the durations begin to overlap.
- Caster One releases concentration on Enlarge/Reduce.
- You complete your animation spell, the Ogre is animated.
- Caster Two releases concentration on Enlarge/Reduce.
- The Ogre returns to Large size.
PHB pg. 212-213; Animate Dead (emphasis mine)
The creature is under your control for 24 hours,
after which it stops obeying any command you’ve given
it. To maintain control of the creature for another
24 hours, you must cast this spell on the creature
again before the current 24-hour period ends. This
use of the spell reasserts your control over up to four
creatures you have animated with this spell, rather than
animating a new one.
That allows you to keep reasserting control of the creature in question as there is no size restriction when using the spell to re-assert control.
It's complicated, but by RAW, you could technically do it.
There is one caveat to this:
The DM has the creature’s game statistics.
A DM may or may not permit you to benefit from the MM stat block for the animated dead. For example, the DM may make the game statistics for a large zombie/skeleton simply be the exact same as a medium one. Ultimately, I would reward a player for doing something creative like this by allowing it since they're exploring magic combinations and castings to achieve interesting results. But that's me personally. The catch here is that the DM will provide you with the creature's statistics.
As a personal home rule: I would permit one of these to exist in exchange for your normal limit of 4. It costs 3 total spell slots and at least three casters to create. In addition, with respect to balance it seems fine. The Zombie Ogre has 4 times the hit points, +3 to it's chance to hit, and on average 4 times the damage. So I would be fine with a player replacing their 4 Zombies with 1 Zombie Ogre.