Who would she marry? One of her lovers? A foreign Prince? Perhaps even the deposed Ivan VI? And assuming she had children what would happen to them? Would they have rights to the throne? Would they be Grand Dukes and Grand Duchesses? Would they still be called Romanovs? Would Paul be conveniently done away with?
1) The Russian monarchy followed some certain traditions and ways. Some traditions were never written down and one of the reasons was that it was not necessary because they were so obvious. Everybody knew them and these traditions were expected to be followed.
You know why the second marriage of Catherine the Great was never discussed or even rumored or hinted in Russia?
- Because it was out of the question. If a woman is a wife of a Russian tsar that marriage is her last one. Period.
2) As for Catherine the Great marrying some of the Romanovs, the male relatives of her late husband...
I guess there is no one in this thread who is an Orthodox Christian or who belongs to an Orthodox tradition.
The Russian Orthodox marriage laws were much much(!) more strict than those in the Western Christianity. The marriage between relatives were forbidden. Sometimes families themselves forgot that they were related as it was so long ago and planned a wedding but when it came to the local Orthodox priest and he found the long forgotten kinship between a fiancé and a fiancée - the marriage was prohibited.
But what important for us here is that according to the Orthodoxy the relatives of your husband (or your late husband) are your relatives - that's why you cannot marry male relatives of your late husband. It was prohibited and followed very severely. All Orthodox Russia lived according to these marriage laws, knew them and followed them.
These rules were complicated and I myself do not know them for sure but my Grandmother knew them all.
So if Catherine had married a relative of her late husband that would have looked like marring your own Father or full Brother - disgusting outrageous incest. That would be illegal.
So if she had married a Non-Romanov she would have been murdered for an attempt to change the dynasty.
If she had married a Romanov she would have been killed for a repulsive filthy incest.