Classification of 10-dimensional heterotic string theories

In many textbooks the typical story is told that there are exactly 2 possible heterotic theories in 10 dimensions, the $E8times E8$ as well as the $SO(32)$ theories. This is of course only true for supersymmetric theories. If one further demands stability, i.e. no tachyons the $O(16)times O(16)$ theory is the only stable non-supersymmetric theory. But if one allows for tachyons much more is possible. In the recent arXiv paper https://arxiv.org/abs/2010.10521 by Kaidi some twisted theories are discussed using a gauging of the $mathbb{Z}_2^5$, resulting in theories with $2^{5-n}$ tachyons where $n=1,ldots,5$. These theories have gauge groups like $E8$, $(E7times SU(2))^2$ or $O(8)times O(24)$. In a footnote the author mentions that these are not all possible theories and one could further allow for torsion in the gauged $mathbb{Z_2}$ groups. Also, this paper focuses purely on theories obtained from twisting the $SO(32)$ string theory, I would assume that similar twists exist for the $E8times E8$ theory.

So my question is: Does there exist a classification of possible heterotic theories in 10 dimensions? Or if this is to broad, are there further known examples besides the ones mentioned above?
Of course the theories should still be consistent in the sense that they are modular invariant and anomaly free. Especially interesting would be a theory with exactly 6 tachyons, which is not obtainable via gauging the $mathbb{Z_2}$ symmetries.