PNGs are lossless so you can’t really dial up the compression. You can save space by reducing to 8-bit color (or grayscale!) but it’s basically the equivalent of raw pixels plus zlib.

PNG can be lossy. It can be done by first discarding some image detail, to make adjacent almost-matching pixel values actually match, to be more amenable to PNG's compression method. pngquant.org has a tool that does it.

There are usage cases where you might want lossy PNG over other formats; one is for still captures of 2d animated cartoon content, where H.264 tended to blur the sharp edges and flat color areas and this approach can compensate for that.