No it would not be illegal. It is done all the time.
The MM firms such as NITE, CDEL, ATDF, etc. have have clients who subscribe to their execution services. The client fills in an application and gets on board. They then make an order or orders and the MM firm executes the order(s) in the marketplace or from their own inventory.
Subscribing retail and institutional clients are in addition to the retail order flow supplied by broker dealers for fee paid by the MM firms.
Here is their web site: http://www.atdesk.com/ - Explore one of the largest MM firms in the world that trade tens of millions of FNMA and FMCC shares a month.