Sculpt Your Distortion
The odds of you finding a profile that distorts just the way you want given your personal tastes, playing style, and guitar specs is extremely unlikely. But just because a profile was dialed-in in a way that doesn't quite work for you, doesn't mean you should scrap it yet.
Use some stomp effects before your stack block to sculpt the distortion tone you want. This can be EQ, a Booster, a Distortion effect, or even a cocked Wah. Bass tends to distort in a muddy, loose fashion, which is why many overdrive and boost effects seek to reduce bass. I like to bring the bass down so that it's barely or not quite broken up - the amp gain will compress it heavily, so you still get a chug sound on mutes, but the bass is well-defined and tight, allowing clarity in quick passages and chords but still sounding big and thick. A big dose of narrow midrange can make the tone sound quite like a transistor (typical stomp box) distortion - too focused and a bit fake. However, midrange is primarily where the distortion is happening - it's what gets the searing, harmonic-rich distortion we love. This is focused around 1 kHZ. A wide boost here will make the tone more "djenty" and squishy. Treble distorts well to a small degree but as you go too high, especially once getting above 3 kHZ, it can start making the distortion get crackly/gritty. I prefer to set a peak EQ around 2 to 2.5 kHZ rather shelving all the high-end upwards. Overdrive units do more than simply EQ the tone, adding their own character to the sound - there's no strong rules here - experiment with different effects to get a feel for them. Distortion effects can add some character to the tone by pushing the signal into a slight breakup which makes the main distortion stage distort a bit differently - usually a bit rougher and with more emphasis on pick attack. But I avoid running them hot enough to become saturated - the result is usually a sloppy mess.
The above generalizations are pretty consistent across different amps and types of distortion; however, every amp is different and require a bit of experimentation to discern how far you can change their character. For example, a Tube Screamer in front of a Marshall definitely changes the distortion from a somewhat rough crunch to a chugging thrash machine. But you're not going to get the same result out of a Fender Deluxe Reverb or a Gibson - you're more likely to get what sounds like you are torturing the amp. Similarly, you can't make a Rectifier sound exactly like a Vox and vice versa.
Kemper profiles are often captured with a real stomp in the signal chain. In these cases I avoid adding another Distortion-based stomp effect - you often end up with too narrow of a focus and things sound fake. However, EQ is fair game and usually quite helpful. Usually such tones will be a bit thin, and I'll use some EQ to fatten the tone up.
The Definition parameter on the amp profile is also directly associated with pre-EQ'ing the signal before the amp distortion occurs. You can crank this up to get a tighter, modern sound (an upper mid-range peak); but I usually go the other way with it, which I find sounds a bit more natural, although less aggressive. If I need to sculpt the distortion tone in such a manner, I prefer to use EQ which I have more control over.
The Graphic EQ is the easiest to experiment with. Keep everything flat then start turning up any particular band and pay attention to the resulting tone. Move it back to 0 and try another band. Now try the same experiment but cut instead of boost. The Studio EQ is also easy to experiment with. Set one of the parametric EQ's to +6 db and adjust the frequency up and down the spectrum. Repeat with a -6 db cut. This will give you a feel for what to expect, then you can focus on improving the tone.
Hill-Climbing
I like to use a "hill-climbing" approach. I make a tweak that I think sounds good and store this as a new rig. Then I A/B the original rig to the tweaked rig. If the tweak is an improvement, I'll delete the original. If I prefer the original, I delete the new rig and start over. I repeat this process trying a few different approaches until it becomes difficult to find any tweak that actually improves the tone. Then I've max'ed out the tone, so to speak - I'm on "top of the hill".
Try Different Cab Profiles
These can totally resuscitate a DOA amp profile. Unless you are trying to get the exact tone of a real rig, there's a 99% chance you will find a cab you prefer over the default one. You can download TillS's cabinet pack here. These are mostly double-mic'ed Marshall 1960 and Mesa/Boogie Rectifier cabs. The Marshalls have some with T75's, some with V30's, and some with G12H's. The Mesa is the stock V30's, and it sounds huge. My personal favorites for the Rectifier cabs are 55, 56, 59, 63, and 66. These sound like there was more of that SM 57 bite in the mix. I also highly recommend grabbing Lasse Lammert's rig pack from the support page and saving the cabinets as presets.
Don't be afraid to tweak the cabinet parameters but remember to hill-climb (see above). High/Low Shift significantly affect the very high and low end frequencies, but also change the very nature of the tone. Start SMALL. I rarely go beyond +/- 0.2 here. Character has more wiggle room. I find increasing it can bring out more of that high-end shimmer, but I sometimes move it downwards too. Again, going too low/high will make the tone sound very fake, but in smaller doses can definitely make an improvement. For TillS Recto cabs, I find they have a particular low midrange roundness or resonance to them that can kind of dominate the tone and make it a bit dull. By lowering Low Shift to around -0.4, this resonance is pushed down to where you can't hear it and the cabs open up and get crispier. Similarly, increasing High Shift a tad (+0.2) can add in the high-end sizzle that is sometimes missing.
EQ'ing - Focus on a Mix Tone
Loop some drums and bass while dialing in your tone. If you are creating a track, definitely re-amp - you will hear things much better when you aren't playing. My philosophy is that a good tone should sound good in all situations - low volume, high volume, inside, and outside a mix. But a great tone will always sound great in a mix at a high volume, and honestly it's more important to sound good in a mix than good solo. Pulling that tone outside the mix and lowering the volume may reduce its charm, but you'll still be able to tell its a good tone. Comparatively, a "killer" tone you dialed up in the headphones at low volume outside a mix is more likely to sound like garbage inside a mix than if you took the opposite approach.
Always set the tonestack (bass, mids, treble, presence) controls before adding a Graphic/Studio EQ effect. Save those for fine-tuning. In some cases you might not need one at all, and this will free up an effects slot.
It's a good idea to browse through the EQ presets that come factory with the Kemper. There's a cut-through-the-mix setting that is a good template to make a tone that doesn't fit a mix fit in. It is essentially boosting around 1.5 kHZ, with smaller boosts to the surrounding areas with more focus around 1 kHZ. I have found moving this peak upwards can get you a thin-sounding tone, but sometimes this works perfectly for a lead, where you want to cut through with a sharp edge to the tone. Sometimes, I find I prefer a lower-midrange peak, but be careful not to add too much of that boominess that resides at the high-end of the bass frequencies.
Another piece of advice is to move the tone stack controls in opposite directions. For example, I may want to boost mids, so I cut bass to prevent too much lower mid-range woofiness or boominess to the tone. Similarly, you can boost treble but back off presence to get a brighter tone but without too much top-end sizzle.
Sometimes tweaking EQ leads you to believe you improved the tone, when what you are enjoying is the added volume. Try to compensate final volume every time you make an EQ change. This will keep you honest about your tweaks.