Having multiple lines, and working out call paths

The current setup is to have calls come in to a main number, ring for 15 seconds, and if not picked up, ring on that phone and 2 additional phones, and if that doesn’t get picked up, go to VM.

Specifically, the front desk phone (Polycom SoundPoint IP650) is assigned Extension 100,107,108,109 and the two additional phones (IP560) are assigned 112,122 and 111,121. The 112 and 111 extensions are meant to be the normal private extensions, while the 121 and 122 extensions are used for the main line rollover.

So incoming calls hit ring group 9000 which rings first available of 100,107,108,109 (so if one or two calls are in progress, on hold, etc there is a spare line to pick it up); then if that isn’t picked up extensions 109 (since it is the least likely to be in use of the four) and 122 and 121 (we have secondary extensions so they can see it if they are already on a call), and if still no pickup then it goes to VM for extension 100.

First, is there a way to have the phones set so they need just one extension, but that they can utilize that over multiple lines? In other words, I’d have the front desk IP650 only show x100, but it could roll over to 3 other slots on the phone for call management. Then I could have the call forwarding just do a hunt on extensions Or am I doing it the correct way?

I don’t know how the Polycom phones handle it, but my Aastra phones do just that.
If you program the first extension with a number, and have call waiting turned on, additional calls to that number will go to the additional “lines” on that phone.