  We present a detailed study of the destruction of SU(N) magnetic order in
square lattice bilayer anti-ferromagnets using unbiased quantum Monte Carlo
numerical simulations and field theoretic techniques. We study phase
transitions from an SU(N) N\'eel state into two distinct quantum disordered
"valence-bond" phases: a valence-bond liquid (VBL) with no broken symmetries
and a lattice-symmetry breaking valence-bond solid (VBS) state. For finite
inter-layer coupling, the cancellation of Berry phases between the layers has
dramatic consequences on the two phase transitions: the N\'eel-VBS transition
is first order for all $N\geq5$ accesible in our model, whereas the N\'eel-VBL
transition is continuous for N=2 and first order for N>= 4; for N=3 the
N\'eel-VBL transition show no signs of first-order behavior.
