There are three ways to handle multiclassing outside the Multiclass Dabbler, Initiate, and Master advancement moves: changing to a new class after level 10, creating a new Playbook that incorporates both classes, or creating a compendium class that incorporates the desired multi-class (Thanks to Slow Dog for that reminder).
After a character progresses past level 10 in their starting class, they have several options. For the purpose of broadening a character's abilities to include those of another class, we want to take the option to Change Class.
Changing classes means keeping your ability scores, race, HP, and
whatever moves you and the GM agree are core to who your character is.
You lose all other class moves, replacing them with the starting moves
of your new class.
Through this process, and with GM approval, the Fighter could potentially keep his Signature Weapon (and maybe his ability to Bend Bars, Lift Gates) while still gaining the benefits of being a Thief.
Creating a New Playbook:
As an alternate to taking either Fighter or Thief, players working with their GM can put together a new playbook that incorporates the features they like from both classes. If you are interested in crafting your own class to fit your vision of your character, it's best not to use a class that is already played by someone at the table. The big worry would be that your new playbook steps on someone else's toes. This is the same justification given for why moves like Multiclass Dabbler act as though they were one level lower.
When adding a move, look carefully at what class it belongs to. Avoid giving a class moves that infringe on another class’s areas of expertise. If the thief can cast spells just as well as the wizard the wizard is likely to feel marginalized. This is why the multiclass moves act as one level lower, so that each class’s niche is somewhat protected.
The third way is by use of a Compendium Class. Compendium classes are sets of moves that allow players to add certain advancement options to their playbooks base. Generally, these require some fictional circumstance to justify the gaining of the compendium class, for example
When you enter the bodily presence of a god or their avatar the next time you gain a level you can choose this move instead of a move from your class: Divine Bond
A compendium class that could potentially work for the purposes of giving the Fighter some of the Thief's moves would be:
Silver City Street Fighter
When you have spent time doing dirty work for the masters of the Silver
City's Thieves Guild, when next you level up you may choose Flexible
Morals instead of a move from your class. If you have done this, when
you subsequently level up, you may then include Tricks of the Trade,
Backstab, Trap Expert and Poisoner in your available advanced
Again, this method only works if you don't already have a Thief in the group since even a compendium class shouldn't be allowing one character to intrude on another's niche.