Could an object around the size of Ceres or even the size of the Moon achieve a stable orbit around the Earth along with our own moon? Would some sort of orbital resonance make this possible?   

As long as it is an orbit far enough from the Moon's, I expect it should be fairly stable. 

I'm not sure how the resonance would have an effect, possibly that could allow a closer orbit.

(all probably what you knew or suspected already)

Can we call this extra moon "Tanman"?

Edited May 23, 20196 yr by J.C.MacSwell

On 5/23/2019 at 6:09 PM, J.C.MacSwell said:

As long as it is an orbit far enough from the Moon's, I expect it should be fairly stable. 

I'm not sure how the resonance would have an effect, possibly that could allow a closer orbit.

(all probably what you knew or suspected already)

Can we call this extra moon "Tanman"?

I was thinking of another large object inside the moons orbit, But my concern was more along the lines of is the Earth massive enough to have another large moon. "Tanman" sounds pretty good.