You've already given the answer, increase the gain like HELL! This is basically the first thing you can do as long as you have the bandwidth, but will give you diminishing returns after a certain point.
It sounds logical and is used in open loop amplifiers, increasing overdrive voltage really increases the linearity. A solid example for that is the current steering DACs where the diff pairs are overdriven with as high voltage as possible. However, there are other factors forcing designers to reduce the overdrive voltage for diff pairs, most important are the matching and noise constraints. As a result most of the high precision opamps have their input transistors operating in sub threshold region. You can refer to Vadim Ivanov's Opamp Speed and Accuracy improvement book.
Another thing to consider is adding source degeneration, there are few ways to do that, all of them will reduce your bandwidth but in the end they will increase your linearity. Actually there are some active circuits used to control the source node to improve linearity.
Other than that, if the high speed is considered, the source capacitance is A PAIN IN THE sitting organs, therefore must be reduced. Funny thing is it is ultimate limitation for third harmonic performance.
But in the end, I did whatever I could, designed a 160 dB gain amplifier with source degeneration and everything, but I couldn't get more than 110 dB THD in 1.8V rail to rail opamp with a swing of 500 mV in 0.18um process. It is not a limitation, maybe I was doing something wrong, it was two years ago so I was kind of inexperienced, but still it should give you an idea.
Regards
