Yes it very much possible to perform single installation on a shared mount and make it accessible from different machines to start server.
suppose we have 3 machines , M1, M2 and M3
we installed weblogic server on M1 at /software mount which is shared between M1, M2 and M3.
Now we create a weblogic domain from machine M1 at /domains mount which is shared between M1, M2 and M3.
Now you configure 3 managed server and 1 admin server as
admin - M1
server1 - M1
server2 - M2
server3 - M3
Now you can simply go on M1 start admin and server1, login to M2 start server2 and login to M3 to start server3.