I'm embarrassed that I never thought of this, but now that you mention it, it seems obvious there would be subsets of emotions other animals feel that we do not. Even if our capacity for emotion is greater, it seems unlikely that the VENN diagram of our emotions and their emotions would show their circle completely contained within ours.

One thing I do think about a lot is what mental capacity other animals have that we do not. An elephant's brain is way bigger than ours. Considering that other large animals have proportionately smaller brains, it must be that size for a reason. I wonder what mental things are easy for an elephant but hard for a human?