Move !lithiumSSO cookie to another domain

Our community has implemented a reverse proxy so our company's domain can be used with a /community on the end for our community address. The issue we are having is that the !lithiumSSO cookie is very large (could be as large as 1k bytes), and we do not want to be passing a large cookie into our company site, since we have a limit on cookie domains.

We have seen an example of another community that used a reverse proxy for their community, and it looks like they have set the domain for the !lithiumSSO cookie to be a variation of their .lithium.com back-end domain.

Does anyone know if Khoros provides support for setting the !lithiumSSO cookie on an alternative domain? Or has anyone run into this issue before and have a solution?