Can a cubic polynomial $f(x,y)$ have two monkey saddles?
A cubic polynomial can have at most 4 critical points and from the inequaility (3.1) in Counting Critical Points of Real Polynomials in Two Variables by Alan Durfee, Nathan Kronefeld, Heidi Munson, Jeff Roy, Ina Westby it follows that at most three of them can be saddles. That this upper bound is attained is shown in Can a cubic polynomial in two real variables have three saddle points? How about monkey saddles, can a cubic polynomial have more than one?