Whether it is possible or not to install a .deb package of a newer Ubuntu version on an older Ubuntu release depends on whether the dependencies required by that package are met on the older release. Anyway, doing so is not supported in any ways.

Ubuntu has other software sources that may or may not contain a newer version. The "proposed" repository contains updated packages for testing, intended to roll out to the main repositories. That would mostly be bug fixes and safety patches, i.e., no major version upgrades. There is also a Backport repository, intended to host packages of newer Ubuntu versions that have been packaged to work with an older release. That may or may not contain a backport of the package you wish. If a package you would wish is not there, proposals for backporting can be made.

Apart from that, you depend on the existence of third party PPA's that may have compiled the newer version for your Ubuntu version. Ultimately, but that requires some (and depending, sometimes a lot) technical skills, one can compile the source code of the newer version of the software.