I wouldn't ask it of my sub.

She wouldn't be allowed to express it with me... so she would have to be open to not being exclusive... and as my sub, she would have to be open to sharing her submissive with me.

Different strokes for different folks.... but no, I wouldn't make her supress it. Whatever makes her her, I don't want to change any of it lest I change what attracted me in the first place.