Is it possible, in an office type synario, to have SER be the 'exchange' for local VoIP clients but for it to also register a user into an external SIP router?

In case that question is not clear:

I have an account with a VoIP provider where if I get my VoIP client to log into their router I can make & receive POTS calls - so people can call me on a land-line number and it arrives at my SIP phone.

But I want to be able to make calls to other VoIP phones in my office area so I want to log my SIP phone into our SIP router and not the external POTS providers SIP router.

I don't want my local VoIP calls to depend on my Internet link.

So what I really want is for my local SER to register me with the external SIP router when I my SIP phone registers with my local SER.

Is this possible?