Two new locations are being considered as possible gypsy and traveller sites by a Devon council.
These are in addition to land already earmarked as a possible site in the Efford area of Plymouth.
The two new sites proposed by the city council are at Coypool in Plympton and Mowhay Road in St Budeaux.
The council said an independent assessment had identified the need for an extra 40 permanent and 15 transit pitches in the city.
There were 25 unauthorised encampments in Plymouth last year, which the council said caused "considerable social tensions" and cost about £160,000.
"We now need to do a lot of talking to a lot of different people"
The proposed site at Military Road in Efford has been under consideration for more than a year and, if approved by councillors, a bid will be submitted for government funding to cover the site's building costs.
Approval will also be sought at a meeting on 20 January to consult Plymouth residents about the two new proposed locations.
Council leader Vivien Pengelly said there was no question of the Coypool or St Budeaux sites being "done deals".
"We now need to do a lot of talking to a lot of different people about the way forward," she said.
"We're very open to any constructive comments which help us to find a solution to this difficult problem.
If approved, there will be a six-week public consultation from 6 February to 23 March.
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