There is no grammatical reason to avoid using as many auxiliary verbs in a sentence as you want. In this case, though, to be is not an auxiliary verb: it is the main verb in your sentence. If you'd rather not use to be twice, you can write: "I study English because it is the language that binds us together."

@P.E.Dant dunno how you analyze it. But I disagree that it's not an auxiliary. It's clearly an auxiliary because it has the NICE property.

Of course be is the main verb in that sentence. Take a simpler one: "[The reason I eat] is [to live]." If be isn't the main verb, what is? Ask yourself the same question about the OP's sentence.

@user178049 Of course be has the NICE properties; but an auxiliary verb need not act only and always as an auxiliary. "I have money." ... "He is Dave." ( "Yes, you have" and "Yes, he is.") I know this disagrees with Pullum. So be it. I think chicken is an attributive noun in chicken soup, too, but the case for the complement is compelling. ;)

"Be" is virtually always an auxillary, even when it's the only verb in the sentence. It's certainly an auxiliary in the OP's excample.

@BillJ You hold with Mr Pullum that be cannot ever be a main verb, but you qualify "always" with "virtually". Does this mean that you see an exception? As you see it, can be ever be a main verb?

This is a tangent, but to put my proofreading hat on, "I study English because it is the language that binds us together" says the same things with fewer words.

@user178049 Calling "be" an auxiliary because it has the NICE properties is confusing and misleading. In ordinary English usage, we don't call the main verb of a sentence auxiliary. Correct would be to say that "A certain esoteric grammar terminology, hardly in use by anybody who knows English, would call 'be' auxiliary here." If the CGEL people wanted to define a category of verbs by the NICE properties, they should have called them NICE verbs instead of redefining "auxiliary". Hell, even computer programmers take more care when naming things.

The term 'main verb' is meaningless, but if you must use it, then of course an auxiliary can be the 'main verb'. All the evidence points to "be" being an auxiliary (with just a couple of exceptions). 'Auxiliary' is a cross-linguistic term and hence justifies its use in English grammar.

@BillJ Let's chat here.

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