I don't know of any law that would limit a company's ability to advertise other products to existing customers.
The idea may occur to you because of antitrust laws, which would impose limits on a company's ability to actually foist extra products on a customer by bundling them together or otherwise requiring their use together. In that analysis, the ability to purchase one product typically has to be dependent on the purchase of another. Simply advertising the product wouldn't do that.
Any law imposing the limits you're talking about could raise some thorny First Amendment issues. Under Central Hudson, laws limiting a company's ability to advertise -- assuming the ads are not misleading and concern lawful products -- must further some substantial governmental interest and do so without restricting more speech than necessary:
The State must assert a substantial interest to be achieved by restrictions on commercial speech. Moreover, the regulatory technique must be in proportion to that interest. The limitation on expression must be designed carefully to achieve the State's goal. Compliance with this requirement may be measured by two criteria. First, the restriction must directly advance the state interest involved; the regulation may not be sustained if it provides only ineffective or remote support for the government's purpose. Second, if the governmental interest could be served as well by a more limited restriction on commercial speech, the excessive restrictions cannot survive.
So if the state was imposing the interest to avoid market concentration or some other antitrust-related interest, it would probably fail because the state could just impose restrictions on the actual accumulation of additional market share or the actual bundling of those products.
Assuming the advertising was legal in other contexts, it's hard to think of an interest that the government could assert to satisfy this test that couldn't be just as well advanced by a less-restrictive means.