Ok, let's think through this problem. What do you need to do? First check to see if the base file exists. You already know the function for that. Since you are performing a decision now, you need a case structure with the select terminal wired to the File Exists? output. In the False case, you just wire the file name straight through.
Now the False case can be interesting. You need to get the various parts of the file path. First, you need the folder. Use Strip Path to get that. Now you need the file name and the extension. Dig back into the Advanced File Functions palette. In there you will find a Get File Extension.vi. That will give you both of these. Now put down a While loop. Inside the loop you will build up your new file name. I recommend using the Format String function. READ THE HELP. It is a very powerful and useful function. Use it to combine your file name, the iteration count of the While loop, and the exention. Then use Build Path to make the full path. Now check to see if that file exists. It is does, keep looping.