I was told that I am the executor along with my partner's son. Is that possible?

A joint executorship is possible, the testator has expressed their wish perhaps because the situation might be difficult if either were sole executor

Who told you?

Heck, I named a whole bunch of executors after the first one, just for the convenience of getting helpers as needed, depending on who lives nearby when I die.
There's no law about it.

Is this your partner's will? Not that it matters.

Yes domestic

In May 2017 you posted:

1. My domestic partner left me her IRA. Her WILL says all other money goes
   To her son and grandkids.

Why are you asking these questions all over again when you had an answer before, at least that is what you posted? Have you never discussed this with said partner?

Anyone can be named executor of some ones will, and any one can be a beneficiary from that will. Wills can be changed at anytime. So sure the possibilities are endless, but subject to change.