The goal of this work is to discover more NP-complete quandles to color knots within the Tait--Rolfsen Knot Table. This presents a randomized algorithm along with two ways in which this algorithm was improved to discover more quandles. The first improvement was to develop a formula for the size of Sharac quandles to tighten the search to acceptable size limits. The second method limits the space of the randomly-selected generator for the quandle to so-called involutory products. Eight new and relevant NP-complete quandles were discovered through these improvements.