Every overdrive pedal will give the amp overdrive a different shape and character. I use a few in front of a Mark V. With the gain on the pedals at 0, whatever tone controls they have become extra tone-shaping controls for the amp sound.
I have a Wampler Belle, Horizon Devices Precision Drive, Tube Screamer mini, and Friedman Buxom Boost. They all give a different flavor to any of the voicings on channels 2 and 3. Well, the TS isn't really good for any low - medium gain stuff, but the other 3 work great with overdrive sounds from ch2 and metal sounds from ch3.
The TS has the most mid boost and cuts a lot of bass. It's also kinda dark on its own, so it's really only good in front of sharp, high gain sounds. But the Belle and Precision Drive will nicely shape any tone, cleans, too. The Belle is an ODR-1 circuit with a bass control and a switch for two types of clipping. It has a 'Color' knob instead of a typical 'Tone' knob, which gives a very different range of tones. It has a slight high-mid boost and low-mid cut. Putting the Bass knob at 0 will tighten the low end as well as the PD. Or it can thicken and sharpen. On 18V with no gain, it makes a nice clean tone enhancement with very little breakup.
The Precision Drive has a 'Bright' knob, an 'Attack' knob, and an adjustable gate. 'Attack' tightens the low end progressively. It's a clicky knob with 6 detents, 1 is flat, 2-6 get tighter. But even on 6, it still retains some thumpy bass (which may or may not be a good thing, depending on what amp/channel and sound you're going for). 'Bright' can get really bright, and can put that sharp squawk into high gain chugs, but it's also great on the Mark I mode, since it's so dark and bass-heavy, the PD can clean up the low end and give it more sharpness and clarity. The gate works perfectly and if it were your only overdrive, you wouldn't need a separate gate pedal. It has a lot of gain on tap, but it doesn't stack well with distortion if you turn its gain up past 1, it gets harsh and gritty. But the amp has plenty enough gain already, so there's no need for extra gain from a pedal. With 'Attack' on 6, it can stay pretty clean, if you want a really sharp, bright clean tone without a big low end. But with 'Attack' at 1 and gain at 0, it has quite a bit of breakup and saturation in the low end.
The Buxom Boost is a clean boost with EQ. It has a 'Tight' knob, Bass and Mid boost knobs, and a Treble boost/cut knob, with a toggle switch to bypass the EQ. I was using it a lot for clean tones with my previous muddy amp, but I don't need it for cleans on the Mark V. It has a wide range of tones to shape channels 2 and 3. This and the 3 overdrives all give a different flavor of the amp's sound. When recording, after I dial in my sound on ch2 or 3, I often stomp thru all 4 pedals a few times to hear each variation, and which one works best for any given part of a song varies.