The General Synod is meeting in York, northern England, the second most important city in the church after Canterbury.
Members will be asked to back a motion calling for a national code of practice to accommodate parishes which cannot accept women bishops.
The Right Reverend John Packer, the Bishop of Ripon and Leeds, will attempt to amend this motion by putting forward proposals for work on two possible ways forward.
One option would be for a national code — but the other would be to explore the creation of a new class of “super bishop” called a “complementary bishop” to cater for objectors.
Under Packer’s proposals, there would be three “super bishops.
Packer’s proposals come amid calls from a significant number of General Synod members for a delay in pressing ahead with legislation to introduce women bishops.
The archbishops of Canterbury and York, the two most senior figures in the church, are understood to favour a compromise that would avoid an exodus of the most conservative wing, The Times newspapaper said.