Unable to mount read-write in OS Catalina 10.15.4 in Single User Mode
Catalina uses a new split-volume system for its file system, where system files are stored on a read-only volume, and user-modifiable parts of the filesystem are stored in a separate "Data" volume that's normally mounted read-write (see this article for more info). But in single-user mode they're both mounted read-only.

If you just need write access to the normally-writable parts of the filesystem, you just have to update the mount point for that volume:

mount -uw /System/Volumes/Data


If you need write access to the normally-read-only volume, things are more complicated. You'll need to:


Restart in Recovery mode and then either make your modifications there and call it a day, or...
Open Terminal (under the Utilities menu in Recovery), run csrutil enable --without fs (see my answer here)
Restart in single-user mode
Run mount -uw / and maybe also mount -uw /System/Volumes/Data
Do your modifications
Finally, restart back to Recovery and run csrutil enable to get the normal system protections back.