We consider $alpha$ corrections to four-point correlators of half-BPS operators in $mathcal{N}=4$ super Yang-Mills theory in the supergravity limit. By demanding the correct behaviour in the flat space limit, we find that the leading $(alpha)^3$ correction to the Mellin amplitude is fixed for arbitrary charges of the external operators. By considering the mixing of double-trace operators we can find the $(alpha)^3$ corrections to the double-trace spectrum which we give explicitly for $su(4)$-singlet operators. We observe striking patterns in the corrections to the spectra which hint at their common ten-dimensional origin. By extending the observed patterns and imposing them at order $(alpha)^5$ we are able to reproduce the recently found result for the correction to the Mellin amplitude for $langle mathcal{O}_2 mathcal{O}_2 mathcal{O}_p mathcal{O}_p rangle$ correlators. By applying a similar logic to the $[0,1,0]$ channel of $su(4)$ we are able to deduce new results for the correlators of the form $langle mathcal{O}_2 mathcal{O}_3 mathcal{O}_{p-1} mathcal{O}_p rangle$.
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