The request is puzzling, and does not make sense. Why would you give a person sole physical in exchange for more time? Primary physical, shared physical, joint physical are just labels. What the court really looks to is the actual time share. However, I never like to give up the words "shared physical."
Perhaps your ex wants "sole legal"???
Please note that this answer does not constitute legal advice, and should not be relied on, as each situation is fact specific, and it is not possible to evaluate a legal problem without a comprehensive consultation and review of all the facts and court pleadings filed in the case. This answer does not create an attorney-client relationship
There are two types of custody in California - physical and legal - with two forms - joint and sole.
Legal custody is the ability to make decisions regarding a child's health, education and welfare. If one parent has sole legal custody then they alone can make the decisions, but the other parent is entitled to all information.
Physical custody is the "possession and control" of the child during certain times. If one parent has sole physical custody then the other parent has "visitation."
State law presumes that parents should share joint custody, and your question indicates that you have that already. The question for you, then, is whether you're giving up more (joint physical custody) than you would be getting (more time). I suggest you contact the court that issued the order and see if they have Mediation or Conciliation Court services to be able to have you and your ex sit down and see what you can work out. If she thinks it's okay for your daughter to spend more time with you then there should be no "payment" for that time; it's what's best for your daughter that counts.
Please note that the answer provided in this forum does not create an attorney-client relationship.
Sign up to receive a 5-part series of useful information and advice about child custody law.