Clayton,
Did your DM by any chance start playing D&D before 3rd edition came out? His need for a story reason for multiclassing makes me think of us old timers who started back with 1st Edition. Back then, if you wanted to be a multiclass character, you chose your classes at 1st level and then leveled them up at the same time, because XP was split evenly between the classes, rather than choosing just one class to level up every time you leveled.
For those that needed a story reason for the changing or adding of a new class when leveling up, groups I have been in generally required you to say what class your next level would be so that you could, in character, be training and practicing for that class as you gained the XP. It also helps if there is another character in the adventuring party that is of the class you are planning on for your next level, as it can be that character who is helping train your character for the new level.
Also, ignore that Warlock/Warlock suggestion, as it is against the rules to multiclass twice in the same class.
Plus, be careful with any Warlock X/Caster X multiclasses, since they do not combine with other casters in the same way, unless they are Pact of the Tome, I think.