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We have recently studied theoretical constraints on the parameters of a 2HDMaugmented with a color-octet scalar. In this paper we consider the consequencesof requiring the model to remain valid up to very high energy scales, such asthe GUT scale. The acceptable region of parameter space is reduced when oneinsists on vacuum stability, perturbative unitarity and the absence of Landaupoles below a given scale. As the scale to which we require the model to bevalid is increased, the acceptable region of parameter space for the 2HDMsector is reduced in such a way that it approaches the alignment limit,$\cos(\beta-\alpha)\to 0$, and the masses of $H^0$, $A$ and $H^\pm$ are pushedcloser to each other. The parameters of the color octet sector are alsorestricted to an increasingly smaller region.

Validity of two Higgs doublet models with a scalar color octet up to a high energy scale