Can SAML and LithiumSSOClient cookies work simultaneously?

Our company has been using LithiumSSOClient SSO cookies for a long time. We want to phase that out and upgrade to SAML. I know I'll have to contact support to configure SAML but I want to be sure that the two options can overlap for a time while we get SAML sorted and an updated website deployed.

Follow-up question. Once we're fully migrated to SAML can we choose to have the old SSO cookies option turned off? Seems like it would be a best practice to reduce the attack surface.