The impedance of an amp affects the overall sound what primarily manifests in the loss of high-frequency content. It can be desirable or can be not. When we add another impedance in the recording chain (like a DI Box) signal changes are inevitable.

You cannot increase the recording chain impedance by adding another parallel impedance, it’s a basic rule. Imagine a huge pipe, water flows freely through it. Then put another pipe in parallel. Despite its size, It can only make the path less resistant. I don’t know how to calculate the pipe resistance, but the calculation of electrical impedance is easy.
For two units, which is the most common situation, Z = Z1*Z2 / (Z1+Z2). So if you have a typical 1 Mohm amp and 1 Mohm DI Box in parallel you’ll get the 0,5 Mohm load for your pickups and it’s too low for the passive ones, which will reduce high frequencies. There are only two options to avoid it or to make it minimal.

The first way is to increase the impedance of your DI Box. 10 Mohm in parallel with 1 Mohm gives us ~0.9 Mohm which is a good result. It’s what Radial JDV and Countryman do.

The other way is to put an active Hi-Z buffer in the chain. It’s how Radial’s distributors work. Pickups “sees” only them and their input impedance, which can be adjusted to mimic different amps.

Both ways have tradeoffs, like life itself. The first reduces the chain’s impedance and loses a fraction of signal what the amp receives (because we need to drive Di Box with something), but it's cheaper and more “pure”. The second doesn’t have this problem and adds extra very useful functions but costs more and put a significant amount of electronics in the chain (but it’s transparent if implemented right).

I use the Radial JX44 distributor in the studio. It eliminates the impedance problem and adds lots of functions as the multi-amp recording and re-amping, fast switching, etc. without perceptible changes in the overall sound. But the Hi-Z DI approach also works fine in simpler conditions.