Abstract: We study the theoretical constraints on a model whose scalar sector contains one color octet and one or two color singlet SU(2)(L) doublets. To ensure unitarity of the theory, we constrain the parameters of the scalar potential for the first time at the next-to-leading order in perturbation theory. Moreover, we derive new conditions guaranteeing the stability of the potential. We employ the HEPfit package to extract viable parameter regions at the electroweak scale and test the stability of the renormalization group evolution up to the multi-TeV region. Furthermore, we set upper limits on the scalar mass splittings. All results are given for both cases with and without a second scalar color singlet.