The deadline for submissions on what the Grenfell Tower fire inquiry should cover will expire on Friday (July 4).
Hundreds of suggestions have been received with the total expected to hit around 300 by the 5pm cut-off.
Inquiry head Sir Martin Moore-Bick promised to consider a broad range of evidence when he launched a public consultation into the terms of reference in July.
Local community members were initially given a week to give their feedback, but the deadline was extended twice.
In meetings with Sir Martin and his advisers, residents have spoken about wanting a team that represents the diversity of the community, with many of those affected from BME (black and minority ethnic) backgrounds.
They also want wider issues and the authorities' response in the aftermath of the disaster to be included in the probe.
Chairman of the nearby Bramley House residents association Samia Badani said: "What is crucial, having spoken to hundreds of people, they want the inquiry to deal with the relationship between the residents and the local authority and tenant management organisation.
"We'd be very disappointed if it was narrowed down on the causes of the fire... we want real change and unless they understand that relationship between public bodies and residents is flawed, there is no hope of this changing."
It is understood that Sir Martin may recommend the Government consider broader questions about social housing separately when he sends his draft terms of reference to the Prime Minister next week.
It will then be up to Theresa May to decide what the scope of the inquiry should be, which she is expected to do the following week.
The deadline comes on the same day as the inquests of three more victims of the blaze.
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