It's possible to run multiple versions of Informatica on Unix. Keep in mind,you have to use different port number ranges, otherwise the domain will not start up. Also, create different installation folders under different Unix users. If you have done that, you should safe to run multiple Informatica versions..
To add to Reza's response, make sure that the environment variables (such as $PATH, $LD_LIBRARY_PATH or whatever is appropriate in your environment, $ODBCHOME, $ODBCINI, $INFA_HOME, etc.) are all set differently for the two environments.
As of my experience - as stated by Reza - you can run two different versions under the same user account, but there are quite a few ways to mess up either installation if you do not pay extreme care.
The safest way I found (and even this way you can easily foul up everything) is to insert some statements in your .profile such that you are asked whether you want to run in environment 9.5.1 or in environment 9.6.1; for example, "read" a shell variable and invoke
if the answer was "log on to 9.5.1 environment", resp. invoke
if the answer was "log on to 9.6.1 environment".
This also has the advantage that you can easily "switch" between these two environments from the shell prompt by simply issuing either of the two commands above.
Again, it can be done, but it is dangerous. Even though I know what to do, I once almost messed up the older installation: I started a certain shell script which (I don't recall why) needed some absolute paths, and so I accidently changed some files in the older environment (because I wanted to start this script in the second installation). Be careful.
Thanks Nico for your reply, I will try the same way as you have mentioned and will see how it goes and let you know.