Separately trademark distinct parts of a trademark to be used in commerce together?

I want to protect various parts of a trademark which parts will be typically used together in commerce, though perhaps not always. If I file trademark apps for each part, will I get protection for a part even if it is always used together with some other trademarked part? e.g. consider a distinctive word, a first distinctive design and a second distinctive design. Let's say that all of these are always used together in commerce. But I want to protect against somebody else just taking one of the three elements and using in an alternate design, or slightly modified, etc. Will I get better protection from applications for each part separately? (I assume I should also file for protection of the composite, but I doubt anybody would copy the composite, more likely copy, or slightly modify, one of the parts). Note that each part is distinctive, not a common word or shape. Thanks in advance for any light you can shed.