Minecraft 1.10 Custom Spawn Eggs

Yes, monster spawners have a SpawnPotentials list, in which multiple different mobs can be specified. Here's an example with a charged creeper and a zombie:

/setblock ~ ~1 ~ mob_spawner 0 replace {Delay:-1,SpawnPotentials:[{Weight:1,Entity:{id:"Creeper",powered:1b}},{Weight:1,Entity:{id:"Zombie"}}]}

For versions later than 1.10, you'l need to replace Creeper with minecraft:creeper and Zombie with minecraft:zombie.

Expanded:

{
    Delay:-1,
    SpawnPotentials:
    [
        {
            Weight:2,
            Entity:
            {
                id:"Creeper",
                powered:1b
            }
        },
        {
            Weight:1,
            Entity:
            {
                id:"Zombie"
            }
        }
    ]
}

The SpawnPotentials contains a list of entries with a Weight integer and a Entity compound tag.

Weight determines how often this type of mob is chosen. In my example, the ratio of creepers to zombies will be 2:1.

Entity is where all of the tags for the entity you want to spawn should go, such as their id and powered:1b.

Delay:-1 makes the spawner immediately pick at random from its SpawnPotentials to copy to SpawnData, rather than spawning whatever's in SpawnData first (a pig, by default).

While the mobcap for regular spawning depends on the number of players, it does not affect spawners.

From the wiki (archive):

MaxNearbyEntities: Overrides the maximum number of nearby (within a box of spawnrange*2+1 x spawnrange*2+1 x 8 centered around the spawner block) entities whose IDs match this spawner's entity ID. Note that this is relative to a mob's hitbox, not their physical position. Also note that all entities within all chunk sections (16x16x16 cubes) overlapped by this box are tested for their ID and hitbox overlap, rather than just entities which are within the box, meaning a large amount of entities outside the box (or within it, of course) can cause substantial lag.

This means that the number of e.g. zombies around a zombie spawner is fixed for that spawner. Even if you bring in zombies that were not spawned by that spawner, they still decrease the amount of zombies that can spawn there. And also it doesn't matter how many players are there, as long as at least one stands inside the activation radius.

I wasn't able to figure out just from research whether the mob spawner counts renamed mobs, too, but from that wiki quote it seems like it.