I used to have one old, bought used, road bike that was a "do everything" bike for me. I got a new road bike as a birthday present. I was considering throwing out the old one and concentrating on the new one, but I decided to wait for a little bit. I ended up stripping the bike down to the frame, overhauling everything, and refitting the bike to make it into my full time commuting bike. My new bike kept it's special status as the "fun" bike. Everyone is happy.
I gotta tell you. Some of the best times I had was the process of refitting that bike. It went from an obsolete 7 speed to an 8 speed with 9 speed components on it's 7 speed hub (basically, take a good quality 9 speed hub apart, take off the upper cog, and assemble on a 7 speed hub to achieve 8 speeds). I rebuilt the wheels. I replaced the handle bars, stem, brake levers, shift levers and rear derailler. By the time I was done, the only "original" components left were the cranks minus the chainrings, the rear hub and the seatpost. I also fitted a good quality rack and full time fenders to it to make it a dedicated commuting bike.
Finally, I got in a slight car accident with the bike which destroyed the frame, so I got a new frame. Now, as the bike sits, the only original renements of the original bike are the rear hub and the crankarms.
The point is, don't throw stuff away. Once you get a new bike, use the opportunity to rebuild the old bike at your leasure. I applaud your decision to keep your old, trusty bike, and remake it into something that will have a nitch in your life!
