This is usually solvable by claiming techniques. For readers unfamiliar with the problem: for a person/company/other entity to directly infringe a method claim in a patent that entity needs to do all of the steps that are positively recited in some claim. If it is a system claim one entity has to deploy, make, or etc. all of the elements of the system claim.
Very often there are multiple "actors" involved in a method. For one entity to be responsible for "A client requesting a data packet and then a server sending a packet" requires the client and server being owned or operated by a common entity. Often the client and server are separately owned or could be to get around the claim. So instead, write "a client requesting a packet from a server and then the client receiving a packet sent by a server". The server is inferentially claimed; it is not "positively recited". Both of the actual required actions - requesting and receiving, are done by the client.
This can be rewritten so only the server's actions are positively recited. Many well thought out claim sets have a claim of the client's actions, a claim of the server's actions and another of the user's actions.
Will this work for you? "A method of determining a person's hair color comprising (a)transmitting an individual's identity to a remote hair-color server; (b)receiving a data transmission from the hair-color server, the data including a code representing the hair color that the individual had previously supplied to the server."
For next level of strategy -- think about which actor you would rather be able to go after. Does one end have more money? Is one part of it something that could be out of the US but the customer and benefit are in the US? Is infringement easier to detect or prove at one end?