Taylor series are famously bad at generalizing and making predictions on out-of-distribution data. But you are absolutely free to add feature engineering on your inputs. It is very common to take the log of a numeric input and you always standardize your inputs in some way, either trying to bound between 0 and 1 or giving the data mean 0 and std 1. In the same way you could totally look at x*y effects. If you don't have reason why two values should be multiplied with each other then you could try all combinations and feed to a decision forest or logistic regression and see if any come out as being very important.