Castle Donington, Barrow, Countesthorpe, and Markfield are the latest bids to be approved.
Barrow is expected to become the first community-managed venue, taking over from the council in July.
The authority hopes communities will run up to 36 libraries while it retains responsibility for 16 of the busiest.
The measures would save the authority up to £800,000 a year from its £5.6m library budget.
Formal agreements are expected to be put in place after legal work is completed, the county council said.
Richard Blunt, cabinet member for libraries, said: "The council will carry out further work with other areas which need more help with their plans, or to encourage groups to come forward in areas where they haven't so far.
"I hope that communities can run all 36 libraries, so that none have to close."
Other community bids where outline business plans have already been approved include Anstey, Glenhills, Kegworth and Market Bosworth.
Leicestershire County Council's cabinet will discuss progress when it meets on 16 June. The meeting will also be streamed online.
A total of 21 community groups are set to take over the running of some of Leicestershire County Council's libraries.