Markbass Distorsore (discontinued) is exactly as you describe.
I've had that, the EBS Billy Sheehan, Ashdown J-Lo, and the Owen Gremlin which all do the same job. Once upon a time I thought that's what I wanted from a pedal too, but it turned out that they all sounded utter pants and so I sold them!
They all have a band pass filter in parallel with your clean tone, and it doesn't sound natural, it's like having an overdriven cocked wah pedal mixed in. And the resulting mid boost makes the low end seem much weaker.
Also I found the EBS unusable unless I put another boost pedal in one of the loops to invert the phase as otherwise the blend cancelled out all the low end. It did sound great after doing this though, but the resulting cable mess was too much faff for me.