Formatting more sectors per track on a floppy was actually more than just a valid method if you did it at the disk level and not just the filesystem level! In the 90s, Microsoft formatted 3.5 inch installation floppies at 21 sectors per track to get 1.68 MB on a disk, thereby reducing the number of floppies needed for larger software considerably.
With even more trickery (like lowering the amount of space between tracks on the disk to get 82 tracks in, and changing the sizes of the sectors on each track) you can get over 1.7 MB on a standard 3.5 inch high density floppy disk. IBM introduced a completely non-compatible format called XDF that pushed the formatted capacity of a floppy to 1840 KiB*. They technically have the space for 2,000,000 bytes of storage on them, but if you just used them raw like that you'd have no way to seek to specific sectors and tracks since those 2,000,000 raw bytes include the space for synchronization information and inter-sector gaps.
* IBM's proprietary XDF distribution format took advantage of the fact that you can technically format different sectors on a single track with arbitrary power-of-two sizes. With 12,500 raw bytes available on a single track, you can fit the equivalent of 23 512-byte sectors onto the track by formatting it as four sectors: the first is 8192 bytes, the second 2048, the third 1024, and the fourth 512. You can do this in the sector ID gaps, but you can't do this in the track header, so the track header was programmed to think there were 39 128 byte sectors instead. This gives you 11776 bytes per track, and with two sides of 80 tracks, you get exactly 1840 KiB. More technical details can be found here