In Florida can my alimony payments be reduced or terminated if my ex is living with someone?

The short answer is maybe. The key is whether a supportive relationship exists between your ex and the person they are living with. If you are trying to reduce or terminate alimony, the burden of proving this situation is on you – the person paying the alimony.
The judge may consider all circumstances surrounding the alleged supportive relationship, but the statute lays out a list of factors to be considered:
1. Whether the couple is holding themselves out as married by using the same last name, mailing address, referring to each other as husband or wife, or any other conduct that suggests a permanent supportive relationship.
2. The length of time they have lived together,
3. The extent to which they have pooled their assets or income,
4. The extent to which one has supported the other,
5. The extent to which one has performed valuable services for the other,
6. The extent to which they have worked together to create or enhance anything of value,
7. Whether they have jointly contributed to the purchase of real property, and
8. Whether either of them has provided support to the children of the other regardless of a legal obligation to do so.
It is important to note that the supportive relationship does not need to involve sexual activity. Also, a supportive relationship cannot exist between family members.