The SAML specification doesn't include any service provider to service provider flows. Instead, flows are between an identity provider and service provider.
Of course, you could perform a simple redirect to the second service provider and it could initiate SSO to the same identity provider. Presumably the user is still authenticated at the identity provider so they wouldn't be prompted to login again.
Alternatively, your application could act as both the service provider and identity provider. As the identity provider you would initiate SSO to the other service provider. This is certainly possible using our library. The SamlProxy example project we include acts as both an identity provider and service provider.