Yes, you can give your character a kit, even if it's not a kit of that class. However! If your character already has levels in the un-kitted class before you alter it with Shadowkeeper, it won't get any of the bonuses. For instance, if you're a fighter7/cleric8 when you hack it to Lathander, you won't get the hold undead or level drain immunity abilities for the first 8 levels. Similarly, if you change your fighter/cleric into a kensai/cleric you won't get the hit/damage/speed bonuses for the first 7 levels. That's because the individual abilities are added on level-up according to kit, so they aren't retroactively applied.*

SO! The best thing to do is to make your character into a single-class kitted cleric, and then use Shadowkeeper to change your character's class to Fighter/Cleric but leave the kit alone. However, in order for your character to be correct, you may have to mess with the three "levels" boxes on the abilities screen of SK. (That's first class/ second class/ third class.) You may also need to adjust your hitpoints values, as they may be too high or too low compared to a "vanilla" multi-class. Things like saving throws or THAC0 may be weird at first, but they'll reset to the correct values as soon as you level up, so don't worry about those. The thing you want to be sure of is that your kitted cleric level before modding is the same as your kitted cleric level after modding, and you want to make sure that the fighter level is 1 or higher. You can then level-up ingame to get the correct fighter level. Make a backup just in case.

It's easier for dual-classing. If you want to dual from fighter to cleric, just go into SK and change your kit to Lathander (or whatever) but leave your class as fighter. Then, when you dual-class into cleric in the game itself, you'll be a Lathander cleric automatically and you'll get all the right bonuses and you won't have to do anything else. HOWEVER! You cannot do this if you're trying to dual-class into a specialist mage. If you try, you'll get stuck on the spell selection screen and won't be able to progress. All other classes are fine, though.


*It's possible to manually add these missing abilities to your character, but you'll need to know how to use IE modding tools, and be comfortable with creating custom items. By adding the class abilities manually, it's also possible to "fake" a character having multiple kits. In one of my recent runthroughs, I played a Wizardslayer/Assassin multiclass that way. He was officially a Wizardslayer/Thief, but with all of the Assassin kit abilities.