The SecureID token come with a fixed built-in secret which only provisioned to the owners idendity server. You cannot authenticate to others with it. And if you could, the admin of the second server could spoof your token on the first.
The only option you would have is to operate the server for both realms by a trusted thirdparty. Like many of the SSO/Login providers.
Sidenote: if you look for other tokens which could be used in such a scenario, TOTP tokens could be re-programmed/seeded. Only problem is I haven't found any which allow more than one seed to select. But for TOTP soft-tokens (apps) this is widely used.