If you're changing pressure, you're changing it proportionally for all gasses. The side which has more moles will have the change at higher power and be more affected by the change.
For example, if you had:
A+2B<==>3C+4D
K=[C]^3*[D]^4/[A]^2
If you double the pressure, you'll double each of [A][C][D]. The quotient becomes:
Q=8[C]^3*16[D]^4/2[A]4^2=16K
To get back to the same K we'll need to decrease the partial pressures of the products and increase the partial pressures of the reactants.