Can I stack ongoing action cards on the same base in Smash Up?
Yes, unless an earlier played action card or minion on the base prohibits that.

In the rules there is a section that states that the rules are not perfect. There will be clashes. And there are some tie-breakers. 


If rule A prohibits X and rule B grants X, rule A wins.
If all else fails, the player whose turn it is decides.