Take the init.ora of the existing db, make relevant changes to it. Create the db using this file. Then either:
1. Take export from existing db, import into the new db.
2. Backup the controlfile to trace. Replace the dbf, redo log files with the dbf, redo log files of the old db. Edit the trace backup of the controlfile and recreate the controlfile using this file, startup the db.
Just clone it, that will be easier and faster.
Take cold backup. Make changes in init.ora file. Take the control file to trace. And make changes to that text file. Copy all of them to the new location apart from all datafiles, logfiles. Recover it on the new place. It should work fine.