Is there a limit to the number of times you can multiclass?

Question

Is there a limit to the number of times you are able to multiclass, for example could you get 1 level in 4 different classes?

Answer 1

Yes. Page 208 of PHB notes:

There are two restrictions on your choice of a class-specific multiclass feat. First, you can't take a multiclass feat for your own class. Second, once you take a multiclass feat, you can't take a class-specific feat for a different class. You can dabble in a second class, but not a third.

This is true for all classes except bard who have an explicit provision to take multiple class-specific feats:

DDI:

MULTICLASS VERSATILITY You can choose class-specific multiclass feats from more than one class.

While the windrise ports background did allow multiple multiclass feats, the recent errata eliminated that option.

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To address your specific confusion, there is no such thing as taking "levels" in other classes, only feats and power-swap feats. In essence, you are always your primary class (though with a multiclass feat you can take prestige paths and epic destinies and class-specific feats for your secondary class, as the feat indicates that you count as a member of that class for game purposes.)