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In the classical sense of "a QFT" then no there are no ways to do QG. The computations diverge. In the extended sense where you let yourself include non-QFT-like things like strings and spin foams, then sure.

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But the fact that the computation diverges is not a problem by itself. All QFT diverge but this can be fixed by renormalisation. Problem is that for gravity this would require infinity many parameters and the theory could match any observation

My understanding was that renormalization only needs "parameters" when the computational methods are approximate.

I thought the issue was more that we have no idea how to perform appropriate calculations for SM+QG? Maybe I'm wrong?

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