These include Octavia Housing, Shepherds Bush Housing Association and Origin Housing, working predominantly in North and West London and the northern home counties.
The group are now looking to set up their third housing framework worth £100m to expanded on the existing stock of 13,000 homes.
Sweet is running the competition to find up to 15 builders for Octavia on the MyTender website.
Previous contractors signed up to the framework include Balfour Beatty, Bouygues, Durkan, Galliford Try, Higgins, Hill, Kier, Mace, Wates and Willmott Dixon.