Most patterns specify a weight of yarn in slightly different terminology, since the number of plies doesn’t necessarily denote the yarn’s thickness. For instance, I have some singles that are bulky weight and some 6 ply yarn that is sport weight. I’m presuming that your 2ply is a lighter weight, maybe sport or fingering, while your 4 ply is a bit thicker, maybe sport to worsted weight. Is that correct?
Either way, if the pattern calls for lighter weight yarn and you prefer a thicker gauge, you could try simply working the pattern but either doing fewer repeats throughout the pattern or work only a portion of the total pattern.
As a very simple example, let’s say the pattern is a triangular shawl worked from the smallest point to the widest point. You could cast on and work the pattern, increasing as stated, until the pattern is as large as you like.
However, if the shawl is square or rectangular and requires that you cast on a whole side of the piece and there is a 10 stitch repeat throughout, you could simply cast on a fraction of the total amount required. Your best bet is to knit a swatch and determine what number would match the size you like, but if you aren’t feeling motivated to do that, you could cast on half or 2/3rds the required number and hope for the best