What you could try is to install it in one of the partitions (say, Windows 10) and then again in the other, but in that one, point it to the existing directory where it was installed in the first OS.
Note that if you have to uninstall it from the first OS, you will have to run a repair install (or uninstall/install again) in the second if you wish to keep it around there, as the uninstall will remove everything. Likely not so if you uninstall from the second OS, because in that case, the installer should have marked everything as already existing and not in need of removal on uninstall, so the install should still work on the first OS without repairing or reinstalling.
Of course, if you don't pay for the second install, even though they share the same set of files, you may be in breach of the EULA. (If the installer calls home to verify the key, it may not even be possible to do the install on the second OS even though your intent is to have it share the same files as the first install and even though, in this case, it's not even possible to use them on both OSes at the same time.)
Update
According to the answer by fixer1234, you won't be in breach of the EULA by installing Office on two different boot partitions of the same physical machine.