Can I add another cable to this 3-gang electrical box?
What size box is it? It should either have a volume printed on it, or will be a standard size. Without knowing the box volume, we can't give you a definitive answer. 

Assuming it's all 12 AWG, it's at least (12 (current carrying conductors) + 1 (grounds) + 4 (device fill)) * 2.25 = 38.25 cu. in. currently. 

Adding another two conductor cable with ground would require an additional 4.5 cu. in. For a total of 42.75 cu. in., not counting any clamp fill not mentioned.

As long as the box is larger than this, you'll be okay. 

Note that if you put the third device in, you'll have to add another 4.5 cu. in.

See this answer for more detail on box fill calculations.