Were there more than two Death Notes?
There were 4 Deathnotes in the real world. Ryuk has 2, Rem has 1 and another of Rem's friend who died to save Misa. Rem gave that Notebook to Misa.

At the beginning of the story, Ryuk gives his additional notebook to Light. Meanwhile after L's death Light got another notebook which was Rem's since Rem also died.

Mello stole one of the Notebooks for which the shinigami came and is supposedly the one originally dropped by Ryuk to be picked up by Light. This still leaves Rem's notebook in Light's possesion and Misa's with her.

TL;DR Humans in the series use 3 Notebooks. Sidoh's orginal which he took back. Jealous's original which Rem gave to Misa and Rem's Notebook which Light picked up after he/she disintegrated.