It really depends on what you're wanting. So like a sub bass you can lowpass the crap out of it and add something like distortion to it post process to get some neat interactions. Knowing I want to do this I tend to test out the lowpass with the distortion added already. Then trying styff like delay or chorus and/or layering in different bands, etc. Unless you're looking for a specific sound or whatever.
The trial and error can be fun. But you're going to want the low end to stay centered and preferable to u, try to keep any delaying on it minimal. Worst thing in the world for me is the bottom end bouncing in the L and R channels one after the other, just because I wanted to get a wider sound out of the upper portion.
Also, mud can come from the mid portion. So try playing around with notching or bell eqing that area.
As far as plugins,. I don't have a lot at the moment. My daw has everything needed to do much of what I need. But there are surely plugins that will do a specific task. Someone may have that information. You could also try googling "stereo widening vst". May be some fun stuff try in your endeavors.
Got to careful adding effects to create wideness. Like chorus or something
You will lose your low frequencies if your not careful. Should be used in extreme moderation with bass
As to not lose its power. Can be used but subtly for tone
If you don't mind mono bass, overdub a sinewave. It's kind of hard to do unless you record the MIDI an octave higher to hear it better. Then quantize it and shift it down and octave or two and freeze it. It can fill in the bass nicely. I haven't done it in a while, but it's a common technique.
For "deep" and "wide" you'll either want two parallel channels or two seperate bass patches. Two channels options: a mono channel for everything under ~150-200hz . Then add stereo widening techniques to the other channel subtracting all the lowend content. Seperate patches for a "top" and "bottom" bass just gives you more control. In that case I usually use a LPF square wave (mono the patch inside the VST synth if possible) for the "bottom" and then saws for the top (HPF).