Your Acme Motor Oil can coexist with Acme Burgers and Acme Bulldozers with little pushback from the U.S. Patent and Trademark Office and little likelihood that any of the other Acmes has a legitimate complaint. Registration should be allowed. What about Acme Antifreeze?
Here you run in to the "Likelihood of Confusion" argument that is the the ban of a trademark attorney's exisitence. While in your mind there is no way that anyone could mix up the source of Acme Motor Oil and the source of Acme Antifreeze, since both are in the sphere of automotive products (both are engine area additives), the USPTO and your fellow Acme supplier may things differently. To mimimize the possibility of rejection and to prepare for the inevitable office action (a note from the Trademark Examining Attorney explaining the probable rejection of the Acme Oil trademark in the face of the Acme Antifreeze mark). you may want to seek an agreement with the owner of the the Antifreeze mark to consent to your use.
A propertly drafted consetn or coexistence agreement can go a long wany to meeting"likelihood of confusion" issues, but it is not a total panacea. There really needs to be some distinguishing features between the two products. For example, I doubt that any consent agreement could handle the confusion issues arising if Hostess, a maker of snack Cakes, had an agreement with the holder of the Hostess Cupcakes trademark. In addition to some distinctions between the two products, the agreement should cover efforst that the companies will make to avoid confusion, cooperatin in the event of confusion and dispute resolutions.
In the even a coexistence agreement would not work, a license agreement may.