Kabouter Games
Explorer
Hiya!
Full Disclosure! : I am quite against MC'ing in 5e (and 3.x/PF for that matter), because I think it's done horribly. (Not gonna get into it here, not the place). But I do have some ideas you may not have considered.
Alright, now then.What I would suggest as another avenue of choice is to really think about what you want your character to represent. Don't think in terms of "D&D choices as per the book". Instead, think of him/her in terms of what he/she could do in a story, novel, movie, etc., if he/she were in one.
Think of what base core class would give a good base feeling. I'm not talking about abilities, skills, etc, per se, I'm talking about "Fighter - tough, strong, action-oriented, weapons, armor, battles and wars, bloodied and battered after a battle, etc". The "essence" of what makes that class, well, 'feel' like that class and not another one.
Ok, take that and use it as your characters Class. Now, work with your DM to create your own Arch-Type that fits your idea, as well as your DM's campaign setting.
IMHO, MC'ing is useless (and badly done) in comparison to the potential of arch-types. Why do you think they keep coming out with Arch-Types in UA and not new classes, or multiclass combos? Because using an arch-type gives them total freedom to create exactly what they are thinking about without trying to shoe horn two or three classes, one particular race, and several particular choices in regards to skills, feats, items, etc. If they feel a concept need to be able to change the colour of skin of the arch-type in question, they just write it up and put it as a special ability gained at Level X. They don't have to force the DM to use Feats and force the character to take some particular Feat that allows him to cast some particular spell that can change the colour of the characters skin.
So...choose a base class, then work with your DM to make an arch-type (or modify one if one is close). Much better than trying to work three classes into a concept that only "mostly" fits your idea.
Say it again for the people at the back.

Cheers,
Bob