You ought to be able to use just about any DAW to do that, although the exact features and capabilities of the DAW can make a difference. The DAW that I generally prefer is Acoustica Mixcraft (which is a Windows-only DAW), and one of the reasons I prefer it so much is that it's so incredibly easy to do what you're talking about. I have a number of other DAWs and most of them can do it, too, but there are more hoops to jump through so to speak.
The idea is to take everything that the keyboard is sending to the DAW on a given channel and divide the events into zones based on the Note values. You send all of the Note events within a particular range to one virtual instrument, then send all of the Note events within some other range to another virtual instrument, and so on, defining as many zones as you want. These zones can be totally separate (which is what keyboard instruments usually call a split), or they can be stacked on top of each other (layered), or they can be only partially overlapping, etc.
Most companies will let you download and run their DAW for free for a limited trial period so you can see how you like it, so you might want to look around to see what's available. Depending on which DAW(s) you decide to try out, I may or may not be able to tell you what you'll need to do to create splits and layers in the DAW.