The Mystery of Banking by Murray N. Rothbard (pg. 118)

On the other hand, if there are only a few banks in a country, and the clientele of each is extensive, then the expansionary process could go on a long time, with clients shuffling notes and deposits to one another within the same bank, and the inflationary process continuing at great length. The more banks, and the fewer the clientele of each, then, the less room there will be for fractional reserve inflation under free banking.