Earlier quoted context omitted.
The language used to describe fractional reserve is pretty misleading. Banks don't increase the total supply of money, all fraction reserve does is keep more of it in circulation. If a bank takes a $1,000,000 deposit one customer, and lends $850,000 of it to other customers, there isn't $1,850,000 worth of money all of a sudden. There is $850,000 worth of debt held by customers, and another customer with a $1,000,000…
> Banks don't increase the total supply of money, all fraction reserve does is keep more of it in circulation. It doesn't increase currency (M0). But is there 'money' in your bank account? They increase money by a slightly broader definition (accounts + currency). Even if you've got a narrower definition (and just want the physical paper to be defined as money, not entries in a database) then they don't increase the…
An advantage of that system was that banks did not lose reserves when customers withdrew money, ie converted deposits to cash.
(The banks lost reserves when those notes were eventually deposited with rival banks who demanded settlement in underlying reserves.)
Of course, even that system did not multiply the amount of reserves; you might call them M(-1), if you are so inclined.
Historically the underlying base money was gold, but you could imagine a system with private bank notes built on top of the federal reserve dollar just fine. You can even leave physical Fed cash in circulation, too.