This is Samuel and I will discuss this and provide you information in this regard.
You are correct CA family code 4323(a)(1) provides:
4323. (a) (1) Except as otherwise agreed to by the parties in writing, there is a rebuttable presumption, affecting the burden of proof, of decreased need for spousal support if the supported party is cohabiting with a nonmarital partner. Upon a determination that circumstances have changed, the court may modify or terminate the spousal support as provided for in Chapter 6 (commencing with Section 3650) of Part 1.
(2) Holding oneself out to be the spouse of the person with whom one is cohabiting is not necessary to constitute cohabitation as the term is used in this subdivision.
(b) The income of a supporting spouse's subsequent spouse or nonmarital partner shall not be considered when determining or modifying spousal support. (c) Nothing in this section precludes later modification or termination of spousal support on proof of change of circumstances.
To begin the process of having it terminated or at the very least decreased, I suggest you fill out
A Request for Order (Form FL-300). You can use the Information Sheet for Request for Order (Form FL-300-INFO) for information to fill out FL-300.
The Income and Expense Declaration (Form FL-150).
If you are changing a spousal or partner support order made as part of your divorce or legal separation judgment, or after the judgment, it may be helpful for you to use the Spousal or Partner Support Declaration Attachment (Form FL-157). You can use additional sheets with information typed if you need more room.
This form asks you to provide the information the judge will need to make a decision in your case, addressing all the factors the law tells the judge to consider when making decisions about long-term spousal or partner support.
This form is optional, but even if you do not use it, you may want to take a look at it to make sure you understand what you will have to prove to the judge.