I have a class with a static factory method on it. I want to call the factory to retrieve an instance of the class, and then do additional initialization, preferablly via c#
Like everyone said, no.
A lambda as an argument has already been suggested.
A more elegant approach would be to accept an anonymous and set the properties according to the object. i.e.
MyClass instance = MyClass.FactoryCreate(new {
SomeProperty = someValue,
OtherProperty = otherValue
});
That would be much slower though, since the object would have to be reflected on for all the properties.