actually u can turn on a group of LEDs, but never more than u have in one row or column (depending on scanning direction) and u won't overcome it. that's how matrix works.
u might use flip-flops ( Flip-flop (electronics) - Wikipedia ) to control relays
that's probably what i would do. say u have 8x8 matrix and want to replace it with 64 relays. u put flip-flops (+some transistors to amplify signal so it would b enough for relays) instead of LEDs and trigger one scanning cycle to program all flip-flops.
just an idea though 