It's not natural. Do you mean, "I offer to do something for you"?
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MustAskI suggest you go with me" sound like an offer"No, it sounds like an advice of subtle warning.
MustAskI'm offering a person a chance to go with me.Why not just say: I'd be delighted if you can go with me.
MustAskI'm offering a person a chance to go with me.Would you like to go with me?