The POD can definitely do this. In fact, when I bought my POD a couple of months ago, I was convinced that I would be using it in preset mode only. But once I got the thing, the footswitches and expression pedal are so useful that I haven't needed to switch presets during any songs. Some songs with crazy FX (Like a Stone with the Pitch Glide is one example) will have their own preset, but within that preset I use the four switches at the top to turn FX on and off. Like you, when I go from clean to distortion I turn off my chorus and turn on the distortion box.
You can also use the pedal to change many parameters incrementally, but I haven't needed this yet. I think that would be useful if you want one amp for clean and another for distortion... you can set them up in different paths and use the pedal to fade between them (while also fading out the chorus and fading in the delay, for example). I haven't needed this because I use the same amp for clean, then kick on the Line 6 Drive for distortion, but it's there if you want it and many people use it.
barks62's post in Assigning multiple events to a single footswitch was marked as the answer