The quickest way I figure that I can get 12 ranks in tumble is by multi-classing into rogue--but the earliest I can get those 12 ranks is at 11th level, as a 4/4/3 ranger/rogue/fighter (7 class ranks via rogue, 5 cross-class ranks via ranger and fighter).

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Is that the only way other than rules alteration?

You only need one level of Rogue to make Tumble a class skill. Page 56 of the PHB: "For the purposes of calculating maximum ranks, a skill is a class skill if at least one of the character's classes has it as a class skill".

So if you have just one level in a class with Tumble as a class skill, your maximum ranks in it are (character level + 3).

If you have Tumble as a class skill (say from a level of Rogue), your maximum ranks in the skill are the same as all Rogue, Ranger and Fighter skills. You buy ranks in the skill at double-cost if the class you raise doesn't have Tumble as a class skill, though (i.e. even though for the purpose of maximum ranks it's a class skill, you still pay double for the ranks if you're "buying" the skill as a Ranger or Fighter).

That said, you'll run into uneven levels multiclass penalties if you don't keep them at even levels. Although since you're 4/2 at the moment, I expect that one of your current classes is your racial favoured class. If ranger (or "highest class") is your favoured class, then you can painlessly add a level of rogue to get Tumble as a class skill. If you can't do it without taking XP penalties, you're probably better off relying on Cosmopolitan.

Take a level of Rogue next level, pump Tumble to ten ranks (assuming you get a skill point bonus of at least +2) - that makes you a Ranger4/Fighter2/Rogue1. Then just raise Ranger levels (to keep the Fighter and Rogue levels within two) and pay double to raise Tumble.

All the relevant info on buying skills and maximum ranks as a multiclass character is on page 56 of the PHB.

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