Can I get bimaxillary advancement for cosmetic reasons?

what I suggest is seeing an Orthognathic surgeon immediately and not wait until ortho is done. There may be a different set up in teeth that the surgeon requires. 

It is not uncommon to see patients where the upper bicuspids have been removed to treat an overbite. It does 'collapse' the upper lip inwards in many cases and leaves a smaller looking lower jaw. Double jaw advancement is possible but there are other masking approaches which can be less surgery; it depends upon your tissue type and even the nasal prominence. Consult  a surgeon at this stage.