What do I buy to use 2line phone and separate fax?

I have two lines/numbers for my business and do not want to add additional lines and cost to my phone bill yet want to maximize the effective use of both lines. Currently, I have DSL and fax only (receive and send) on one line utilizing an HP all in one machine. I do not currently call out or receive calls on this line other than faxes period. The other line simply has a phone with answering machine. I do not want to change the numbers that my customers utilize currently to fax or call to talk as they are familiar with them, etc. My question is simple: Can I buy a two line phone and get more use out of the now fax only line without disrupting fax receiving, hanging up on calls, etc.? Do I need a splitter? Something or anything else? Do I change the settings on the phone and or fax to a particular function setting? My main objective is to utilize the now fax only line for incoming customer call overflow and transfer customers to different people within our office to respond to their particular needs using a cordless handset and the other line (ie now fax only line).