Should GvK risk leaving on a cliffhanger?

They probably shouldn't end on a cliffhanger, because if they tease another monster or anything that could lead into a sequel, and the monsterverse ends, then it will leave people disappointed and it would feel like a unfinished story that was published anyway.

Probably not, considering the popularity of the monsterverse is not good atm aside from Godzilla fans. I really don’t want GvK to take the BvS route with the surprise villain either. I feel like they should make one more movie after GvK though. Destroy all monsters. Have the head be revived using radiation and dna from other titans making a human created titan. Have it hunt down and kill titans until the remaining ones have to jump it. Kong would join in too because I don’t want him to die in GvK. I do think he will lose but he is going to give Godzilla the beating of a lifetime before going down.

I doubt that it will.

Any ideas on how to add a third monster without ruining the plot?

To add a third kaiju, the Number 1 thing to get right: Don't spoil the surprise in the trailer. Advertise it as a throw down for the ages, actually deliver on that before the 2-hour mark, then have the final team up be a cherry on the smackdown sundae. Basically the opposite of everything BvS did after the first teaser.

As for actual plot stuff, don't have Godzilla Vs Kong be engineered by the humans in any way. Have it be an inevitable territorial/dominance dispute separate from the human plot about Titan origins and conspiracies, that way the humans can slowly and organically discover the big bad monster all while trying to scurry around a fight they didn't start and can't stop. In the end the monster awakens/activates and causes such a major upset that it forces Godzilla and Kong to switch gears, probably right before the winning blow. Then since both are severely weakened from the movie-long brawl, working together will come as a necessity to ensure survival. 

Theoretically all this will keep the stakes of the main battle real, and not make the third monster feel like just a third-act plot device but a natural endpoint to the plot. I think anyways.

Probably not.

I dont think that there should be a cliffhanger but do not have Kong or Godzilla die in there epic battle, if they do another one have them team up with some of the other favorites if possible against another Kaiju or two.    Monsterverse is coming back and if you leave a cliff hanger and dont make another movie people will be upset since it could be a long time before another movie is made.