Maybe an overdrive pedal is not the best choice for you.
Every overdrive pedal has got its very one sound character.
Some emphasize the mids, others cut off the low end because, especially in combination with much gain, too much bass may cause a boomy tone.
Although many guitarists always search for a low gain overdrive pedal, this range is the weak point of this kind of stompboxes.
Booster – the better overdrive pedals
Especially, when you are looking for a transparent or sound-neutral overdrive, it sometimes is worth it, to try a boost pedal instead.
As the name suggests, booster are able to boost the guitar signal.
An amplifier that produces sounds which are close to the borderline between clean and overdriven sounds, can be driven into saturation with a booster pedal and therefore make an overdrive pedal superfluous.
Single coils with little output can be boosted in a way that they sound more like humbuckers.
The louder the signal that gets into the amplifier, the better the (tube)amp will sound.
If you want to create the distortion right on your pedalboard, you can stack two boosters together.
By activating only one booster, the signal will be pushed and the amplifier sounds louder and more powerful.
A second booster acts like an additional gain stage.
The first booster drives the second one into saturation.
And because booster pedals are not supposed to be overdrive pedals, they provide a high clean headroom and you can also create nice low gain sounds.
On top, they are more sound-neutral than most overdrive pedals.
And if you are looking for a pleasant mid boost, you should reduce treble and bass while you increase the volume.
So, if your favorite overdrive pedal has too much gain and effects the signal too much, you can replace it by two good booster pedals.
By this you might get closer to the sound you are looking for.