For people wanting a small number of DID lines with a Partner that has spare CO or station ports you can use a device like this without resorting to a T1:
https://www.multitech.com/PRODUCTS/Families/CallFinderDID/ Data sheet here:
https://www.multitech.com/DOCUMENTS/Collateral/data_sheets/86002055.asp Each device supports 2 traditional DID lines and you can add more to the Partner system as long as you have more ports.
Basically, you map each DID number to an extension number in the device and setup other parameters.
If you have spare station ports: When a call comes in the device takes the station port off hook and (with Automatic Line Selection (ALS) for the port set to Intercom) sends touch tones for the corresponding extension to make a transfer.
If you have spare CO ports: You will need an Automated Attendant (AA). Technically, an ASA/DXD card would work but I think someone with DIDs would also want voice mail covering incoming calls. When a call comes in the device generates a ring and then sends touch tones for the corresponding extension.
I hope this helps. I should probably add: I am not connected with the manufacturer in any way, I don't sell these, this isn't a solicitation, and it could be that other companies make similar devices.
-Rob