Myself and my wife have an office W7 laptop each and while at home we share a common Internet connection and use a Belkin wireless router. Our problem is that we can't connect simultaneously to our separate offices through VPN connections. Each of us can connect one at a time. When the other attempts the already established connection always drops.
It may not be possible, at least not without replacing your router, as you have no control over the server configuration so can't alter one of those to not conflict.
To know why there is a conflict (and if there is a way to resolve it) you'd need to tell us much more detail about the VPN you are using: the name of the client software and any connection configuration (apart from the server name and your login credentials of course: we don't need those and stating them in a public forum would be, erm, problematical!).
Standard home routers use a subset of NAT to share a single public IP address with the internal network. This works well for most TCP based protocols but unfortunately most VPNs are not based on TCP connections (for various reasons it is less efficient, and sometimes less reliable, than other methods). It can work well for UDP too, though some routers can be a bit dim in this regard. If your VPN uses some other IP protocol though then chances are your router is doing nothing more clever than simple pass-through, which translates as little as possible in order to get the packets out and generally can't cope with more than one connection running the same way - either one machine stops getting responses when the other starts, or both get a mix of responses and both connections become unreliable. A more intelligent router might have specific support for your VPN's chosen protocol, but you may have to ask your company's IT people for help there (they may be able to recommend one for you that other users under their control have tried).
Switching protocols at your end is not going to help unless one or both of the remote end-points support more than one protocol already - your client end-point can't simply request protocol support that has not been specifically configured.