We prove that coNP ⊆ MA in the number-on-forehead model of multiparty communication complexity for up to k=(1-ε)log n players, where ε>0 is any constant. Specifically, we construct an explicit function F:(\0,1\ⁿ)ᵏ→\0,1\ with co-nondeterministic complexity O(log n) and Merlin-Arthur complexity nΩ(1). The problem was open for k≥3. As a corollary, we obtain an explicit separation of NP and coNP for up to k=(1-ε)log n players, complementing an independent result by Beame et al. (2010) who separate these classes nonconstructively for up to k = 2(1-ε)n players.