4G LTE: Is it possible to make a high gain antenna that resonates well for two frequencies, where one isn't a close harmonic of the other?
Yes, that's possible, and you'll find directive multi-band antennas commercially-off-the-shelf.

These internally mostly resemble Yagi-Uda antennas, but don't have the same director sizing as actual Yagi-Udas. Probably, they were designed starting as Yagi-Uda, and then stochastically optimized in simulation until they worked well enough on multiple frequencies.

By the way, this 90% already was covered in the answer about feeds to your last question.

So, 


  is it possible to make...


yes; whether or not it's possible for you depends on your willingness to learn how to simulate complicated antennas and your access to tools to build and to measurement chambers and costly measurement equipment to measure an antenna.

Really, buy a multi-band antenna. These exist.