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.
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.