Multiple Interfaces modifying contract
I think if you continue this path you violate the "interface seggregation principle". Try to separate the interfaces. Going with your semantics I expect interfaces like ParameterAware or Storable. Then you won't get into such a semantical trouble.

As you have less semantical problems with your interfaces  you will face other challenges that have to do with the implementing classes and your algorithms using and working with these seggregated interfaces. But you cannot escape it and the effort and it is justified.