Chain would be sometimes worn under plate (especially the kind that covered only part of the body), but usually it would have been some form of padded jacket (which can be made in a way that would make it a half-decent armour in its own right), to prevent bruises and scratches. Typically, wearing two different types of heavier armour would be too impractical, for reasons like excessive encumbrance or limited mobility. That, and a warrior who could afford two sets of armour would probably simply consider getting one, but of higher quality, instead of putting on both of them.