I have a bad feeling about this. There are two reasons, that I will get into, presently.
First let us look at a scenario, where one player has three teams (4 when chassis development comes in as well). That one manager will, eventually, be able to supply all of their teams with all of their maxed out parts. This sounds fair, but it basically negates your idea of the suppliers being independent. In my opinion, this will, effectively, overpower all of this one person's teams. This is my first reason.
Then, if you want to police against this over powering of teams, it will have to be done by tracking user ip addresses. If the player is managing from the same dwelling /mobile device, then the same ip address would show for each of those teams. Unfortunately, this has been negated by the use of Virtual Private Networking apps. Where you can have all three (or four) teams appear tens of thousands of miles away from each other, even though they are all being managed in the same room. That with no means to leagally track back. This is my second reason.
My opinion is to do something like you suggest, but just allow every team to get them all.