  We introduce {\it conformal multi-matrix models} (CMM) as an alternative to
conventional multi-matrix model description of two-dimensional gravity
interacting with $c < 1$ matter. We define CMM as solutions to (discrete)
extended Virasoro constraints. We argue that the so defined alternatives of
multi-matrix models represent the same universality classes in continuum limit,
while at the discrete level they provide explicit solutions to the
multi-component KP hierarchy and by definition satisfy the discrete
$W$-constraints. We prove that discrete CMM coincide with the $(p,q)$-series of
2d gravity models in a {\it well}-{\it defined} continuum limit, thus
demonstrating that they provide a proper generalization of Hermitian one-matrix
model.
