Do later phases enable summoning stones?

Not all the time. I had to search high and low for “how often must I engage in combat, for me to learn the pet skill”. 'Cause Petopia tells you to tame those pets (with the specific skill you want) and then engage in combat. But it fails to tell you, “you may need to do this, for awhile”:

I “necro’d” a 2 Month Thread. People forget, the ones “necroing” are actually using Google. 'Cause Google doesn’t pop up new Threads. Only old ones.