The Am9 chord is basically an Am7 chord with the added 2nd note from the A natural minor scale (Aeolian mode). The 2nd note in the Am scale is "B". The reason the chord is referred to as Am9 is for tonal value, but the 9th is the same note (B) as the 2nd, an octive higher. To figure out the relative values of the Am9 chord, look at it's make up. Am9 = 1-b3-5-b7-9, notes A-C-E-G-B
Right away you can see that all of the notes are natural (no #/b's). So, we know that C Major it's cronies are a given.
C Major = C-E-G
C6 = C-E-G-A
CMaj7 = C-E-G-B
CMaj9 = C-E-G-B-D (D works because it is a Perfect interval (P4)of A)

there's more but You get the Idea, what else works beside C?
G Major = G-B-D
Dm = D-F-A (F works because it's the b6th of A natural minor scale)
Em = E-G-B
FMaj = F-A-C
Bm/b5 = B-D-F (used rarely by some because it's a diminished chord)

Although there are more than stated, You can see the relationship.

What about FMaj7 or FMaj9, would they fit?

Would EMaj7?????