1,200 signatures were added during Saturday's Championship game against Ipswich Town, and campaigners - Iron fans, backed by the Football Supporters' Federation - will be present again on Tuesday night when Barnsley visit.
The campaign was started by Iron fan David Beverley in response to Government regulation that states clubs cannot compete in stadiums with standing areas once they have completed three years in the top two divisions.
That means the terrace must be seated or closed should the Iron avoid relegation to League One this summer.
United have plans to redevelop the Doncaster Road End, but with proposals not yet submitted to North Lincolnshire Council for planning permission and funds not in place it is much more likely the club would simply add seats to the stand, reducing capacity to 8,003.
The Liberal Democrat political party have previously supported safe standing areas, and the change in Government earlier this year to a coalition with them as a junior party has raised hopes of a change in the law.
There is also the precedent set by Cardiff City's Ninian Park, which was allowed to keep its terrace for three seasons beyond the limit.