@EnergyNumbers has said the answer in the comments but I want to make it crystal clear what it means as I think this misconception of fractional reserve banking may be widespread.
First, banks can lend to other banks. There is no shell company involved unless for some other reason.
Second, banks can lend to other banks, which then can lend back to the original bank, which then can lend to other banks, etc. How long can this process go? Infinitely - assuming your currency can be infinitely divided.
Then an infinite amount of money is created, right? No. At each step in this process the amount lent out is decreased. If your reserve requirement is 20%, then you can only lend out 80% not 500%. The following is a table from the Wikipedia page on the money multiplier that illustrates this process:
So at the end of the process, what is the maximum amount generated? The inverse of the reserve requirement: in other words, for a reserve requirement of 20%, it will be 5x. Note this is not 5x per step but 5x at the end of an infinite number of steps.