  We have recently studied theoretical constraints on the parameters of a 2HDM
augmented with a color-octet scalar. In this paper we consider the consequences
of requiring the model to remain valid up to very high energy scales, such as
the GUT scale. The acceptable region of parameter space is reduced when one
insists on vacuum stability, perturbative unitarity and the absence of Landau
poles below a given scale. As the scale to which we require the model to be
valid is increased, the acceptable region of parameter space for the 2HDM
sector 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 pushed
closer to each other. The parameters of the color octet sector are also
restricted to an increasingly smaller region.
