  We introduce and study a system of coupled nonlocal nonlinear Schr\"odinger
equations that interpolates between the mixed, focusing-defocusing Manakov
system on one hand and a limiting case of the intermediate nonlinear
Schr\"odinger equation on the other. We show that this new system, which we
call the intermediate mixed Manakov (IMM) system, admits multi-soliton
solutions governed by a complexification of the hyperbolic Calogero-Moser (CM)
system. Furthermore, we introduce a spatially periodic version of the IMM
system, for which our result is a class of exact solutions governed by a
complexified elliptic CM system.
