You CAN play cross harp on a chromatic, the layout is the same for blow / draw notes and the slide just shifts to the alternate bank of reeds, usually a half step from the non-actuated harp so all the sharps and flats are available.
The larger question is why you would want to do that.
Most every harp player who plays cross harp uses reed bending technique, which is very hard on the reeds. Chromatic harps are EXPENSIVE so most harp players use them as they are intended to be used and stick to cheaper harps for blues.
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