Most things are possible.
I will suggest a set up that will work for you in the moment, but, having been through the process of marrying Asterisk with my Panasonic PBX, it would have been a lot easier in retrospect to just start afresh with 100% Asterisk based system. Which I have moved over to now anyways. This is what I recommend you do.
Presumably you have your Dialogic 1000 Media Gateway is there to route calls for your Toshiba PBX to/from a VOIP service provider. You can also configure the gateway to register to your Asterisk server.
So steps would be something like the following:
- Register your Dialogic gateway with your asterisk box
- Program toshiba/dialogic (can be speed dial) to dial out to asterisk, and asterisk can connect that call to a SIP extension.
- Program Asterisk dial plan so that when your Toshiba extension numbers are dialled from your SIP phones, asterisk calls your Toshiba. Your Toshiba can route the call to an toshiba extension similar to how it would handle a DID number. You can program the caller id headers in asterisk etc.