Lloyd's chairman Sax Riley has warned dissenting Names that to reject his reforms would be a "grave disservice" to the 314 year-old market.
Opposition has been mounting to the vote on the Chairman's Strategy Group (CSG) proposals taking place today at Lloyd's.
Riley has asked Names to put aside their grievances for the good of the market. He said the fate of Lloyd's and the Names are "intertwined".
But one leading Name will use the EGM to call for Lloyd's chief executive Nick Prettejohn's resignation.
David Mainwaring accuses Prettejohn and the Council of Lloyd's of "dishonesty" over its handling of the Jaffray Names litigation and the "unreliability of its solvency certificate".
The largest Names' association - the Association of Lloyd's Members (ALM) - came out against the proposals last week.
Members' agent Christie Brockbank Shipton (CBS) also sent a letter to its members on 4 September recommending they vote against the proposals.
CBS told its Names: "Our decision to vote against the resolution is because it seeks to embrace changes to the capital structure which are at best unclear and ambiguous."
On 3 September Hampden Agencies also advised members to oppose the vote.
Most Names support the franchise proposals but concerns include the proposal to eventually ban unlimited liability and worries over Names' protection.
Littlejohn Frazer insurance partner David Roberts said: "The original proposals that were aired but not published had a number of proposals that were regarded as anti-Names. Lloyd's abandoned these... but our view is that they still want an end to third party capital."
There is also concern over the proposal to pass a new Lloyd's Act, but Lloyd's has made clear that passing the resolution at the EGM will not facilitate this - the proper parliamentary process will have to be gone through.
It is widely thought the EGM vote will be passed, but that mounting opposition will make Lloyd's cautious about more contentious proposals.