When you run chmod +x+r+w file, all the bits are set, except those masked by your umask. Your umask presumably masks (at least) other users’ write bit, so the +w part ends up being ignored for them.
Thus for a typical umask of 022, any chmod command which doesn’t specify who the permissions should be set for ends up ignoring any specified changes to the group’s and others’ write bits.
To set all the bits, ignoring umask, you need to specify who you want to set them for:
chmod a+rwx file
or more explicitly,
chmod ugo+rwx file
(or any subset of ugo, as appropriate, for the user, group, and/or others).
It’s also possible to specify numeric permissions instead of symbolic permissions; see Understanding UNIX permissions and file types for details.
Note that the umask masking behaviour also applies when clearing bits, which can produce surprising results: chmod -w file will only clear write bits which would be set by chmod +w file! Continuing with a typical umask of 022, this means that chmod -w won’t touch the group’s or others’ write bits, leaving them set if they already are. (GNU coreutils’ chmod helpfully warns about this.)