The agency is going out to consultation with contractors after previous framework deals were criticised for being too main contractor heavy.
It has also run into problems with some current framework arrangements, particularly for smaller refurbishment and improvement projects, where contractors have turned down mini competitions because they are too busy.
At the same time several local authorities have shunned the EFA’s panel of pre-tendered contractors to set up their own bespoke lists of firms or use independent arrangements like Scape.
To tailor the framework and gauge the appetite for a revamped arrangement, the EFA is planning briefings in Nottingham on the 20th and 22nd June.
Just 10 builders were placed on the existing £4bn national framework three years ago.
Industry bug guns like Balfour Beatty, BAM, B&K, Carillion, Galliford Try, Kier and Sir Robert McAlpine secured placed on both north and south geographical lots.
The EFA said the exact set-up of the new £6bn construction framework has still to be finalised but under present plans around 30 places would be available for contractors across several lots.
The new line-up of firms will be used for the delivery of EFA capital building programmes, including the priority school building programme, free schools, university technical colleges, studio schools and academies capital maintenance funded schemes.
Interested firms must register their interest at the EFA web portal no later than 6 June.