Yes you can. But you need updated Mono also. Then, you can compile it (if it doesn't depend on something else besides mono.).
(Usual way:
1) sudo apt-get build-dep monodevelop build-essential
2) cd /where/the/monodevelop/source/is/
3) ./configure --prefix=/usr
#here you configure it up. Type ./configure --help
to see your options. It'll also check for dependencies, it'll tell you if you still miss something.
4) make
#basically you make the binaries in this step
5) sudo make install
#this will actually install it
(NOTE! I wrote the "usual way". There is no guarantee that this will work. Make sure you READ the README/INSTALL file in the source folder of Monodevelop. Also, keep the source folder (what you used for install). You will be able to delete it later using this folder and issuing the command: sudo make uninstall
.)