As bizarre as it sounds the demand can be outside the scope of the patent infringement. You are right, that typically a cease and desist would be along the lines of: 1. you are violating our registered patent(s), 2. we demand you cease and desist and/or begin paying royalties and past royalties calculated to be "$x".
However, you can be very creative and tack on other demands unrelated to the patent infringement. One very important point here, regarding settlements and settlement offers, parties to a lawsuit are prohibited from disclosing settlement offers/settlement discussions to the Court (again like all things in law, this is the general rule and there are exceptions, example if someone violates a settlement agreement and you sue to enforce said agreement obviously you disclose the confidential agreement to the court).
However, you can be very creative and tack on other demands unrelated to the patent infringement. One very important point here, regarding settlements and settlement offers, parties to a lawsuit are prohibited from disclosing settlement offers/settlement discussions to the Court (again like all things in law, this is the general rule and there are exceptions, example if someone violates a settlement agreement and you sue to enforce said agreement obviously you disclose the confidential agreement to the court).