Best practice for encapsulating a parameter that requires multiple interfaces to be implemented

^{First of all, Iterate is a lame name for that interface, it should be called Iterator, so I will be calling it Iterator in this answer, because I am allergic to bad naming.}

You say that you encounter this issue often, and I have to believe you, but I also ought to mention my experience, which is that I have rarely, if ever, encountered this need in the last couple of decades that I have been doing OOP.

Usually, when such a need appears to arise, it is an indication that some other aspect of the design needs refactoring.

The first suspect to examine is the CopyTable() function: why does it need both an Iterator and a Streamable for both the source and the destination table? Why can't it just stream-out the source table to bytes and then stream-in the bytes into the destination table? And why is it even called CopyTable when it is probably just CopyStreamable() or CopyStreamableIterator() at worse?

If there is nothing that can be done about the function, then the best approach in my opinion is to combine the two interfaces into one. The name CopyStreamableIterator() which describes what the function does immediately tells you that you need a StreamableIterator interface which combines Streamable and Iterator. There is nothing wrong with that, and you do not even have to make your Table class implement that new interface, you can simply implement a StreamableIteratorDecorator (see decorator pattern) which accepts a Streamable and an Iterator as constructor parameters and implements the StreamableIterator interface by delegating to them. (Though you will probably just declare your Table class as implementing this interface to be done real quick, because your Table already implements these methods, so it is good to go.)

_{Note: I am presuming that in Delphi, just as in Java and C#, a class may extend only one class but multiple interfaces, and that an interface may also extend multiple interfaces, but even if by any chance this is not true, this functionality can be emulated by aggregating interface implementations into classes and adding to classes and interfaces methods that return sub-interfaces.}

Amendment

Thinking about it a bit more, I am realizing that your problem may lie in that ill-named IIterate interface. This interface is trying to cut corners, so it is built in such a way as to force manipulation of the internal state of the underlying (implementing) object. This causes problems, because it is forcing you to have two separate interfaces, one for altering the internal state of your table to select a row, and another interface for reading/writing the currently selected row.

In a language like C# and Java your table would implement IIterable<IStreamable>, and IIterable<T> would have just one method, newIterator() : IIterator<T>. In turn, IIterator<T> would be defined as follows:

IIterator<T> = interface //javaesque
  function Next : T;
  property EOF: boolean;
end;

or as follows:

IIterator<T> = interface //csharpesque
  function Current : T;
  function HasNext : boolean;
  procedure MoveNext;
end;

So, instead of selecting rows, your iteration would be yielding each row which can then be streamed. So, you only need to pass an iterator (or better yet an iterable) to your CopyTable() function.

Adding rows to the target table can be easily accomplished by implementing a IConsumer<IStreamable> interface which simply appends the contents of the IStreamable as a new row at the end of the table.