Suppose you have a structure with universe $M =\{a,b,c,d,e\}$ with unary predicate symbol $P$.
Suppose $I(P)$ is the set containing $a$ and $b$.
I found the set of definable sets without parameters to be: the sets that have the property P, don't have the property P, the intersection of the two (empty set) and the union of the two ($M$).
What about definable with parameters? How would would you define the set containing $a$, $b$, and $c$ for example?
You can define every set with parameters since $M$ is finite, and you don't need the $P$ to define them. You just need a equality symbol. For example, consider $A=\{a,c,d\}$. You can define $A$ by a formula $$(x=a)\lor (x=c)\lor (x=d).$$
If you don't have the equality symbol in your language, you can only define sets you mentioned in the question, even if you allow the parameters.