First of all, what you are describing is not quenching but just simple dissolution. Quenching in chemistry means "stopping a reaction" or "decomposing reagent". It is used in (often) cases when one of the reagents in the reaction are somehow dangerous when worked up using common techniques or hard to separate. For example, suring H2O2 oxidations (such as preparation of N-oxides or bayer villiger reaction), evaporating the mixture with peroxide present is very dangerous due to possible (and very real) posibility of explosion. In that case, reductant such as Na2S2O3 which reacts with the peroxide and decomposes it which makes the reaction safe to evaporate.
Anyway, soubility of KOH i water is 120g/100ml at room temperature. The dissolution is quite exothermic, I suggest adding the hydroxide slowly while cooling and stirring, otherwise the hydroxide gets stuck at the bottom of the beaker.