A report going before this month's General Assembly recommends its 800-plus delegates, or commissioners, support keeping a compromise deal reached last year over allowing gay ministers.
The report and a related Kirk proposal over how the Church could implement gay ordination laws will be the focus of commissioners, including ministers and elders, on the same day at the week-long gathering in Edinburgh.
The tandem reports are the next step towards the long-term fix over gay and lesbian clergy.
One of the documents, compiled by a specially commissioned Theological Forum, urges unity in the Kirk, which has been riven over the issue since the appointment of openly gay Reverend Scott Rennie to a church in Aberdeen in 2009.
Since then, 13 ministers and proportions of their congregations have left the Kirk, including five in the last year when the current stance was adopted. It represents 1% out of 1389 congregations.
The report says the current position "offers greater transparency and legal security than an uncomfortable 'don't ask, don't tell' policy".
The forum asks members to back the compromise proposal, which means congregations would uphold traditional teachings to employ heterosexual ministers but others could take on gay and lesbian ministers with enough congregational support - a position described as a "mixed economy".
The separate proposal, or overture, set out by the Church's Legal Questions Committee, looks at how the Kirk could implement its compromise and tackle issues such as what would happen to a minister who later entered into a civil partnership after being appointed.
It says if there is not enough congregational support through the Kirk Sessions "then the pastoral tie shall be dissolved or appointment terminated".
Some evangelicals considered the compromise move last year as placing the Kirk on a trajectory towards fully accepting gay clergy and challenges will be expected from the floor of the Assembly.
If agreed by commissioners, because of the legal nature of amending church law, a mechanism known as the Barrier Act will be invoked, taking the issue back to the presbyteries for a separate vote in December and possibly on to next year's Assembly.
The Theological Forum was set up last year and its convener is Iain Torrance, a former Moderator Of The General Assembly Of The Church Of Scotland.
Its report said: "Any settled consensus is unlikely to be achieved in the foreseeable future.
"The unity of the Church often needs to withstand deep disagreement and to provide safe space for honest and sometimes painful exchanges."
Pauline Weibye, secretary to the Council Of Assembly, said: "The General Assembly of 2013 asked the Church to find a way of incorporating a 'mixed economy' into Church legislation. The overture to be considered on May 21 explains how that could be done.
"The report of the Theological Forum, which will also be considered that day, describes how the Church Of Scotland has lived with differences of opinion before and advocates 'constrained diversity' on the issue of the ordination of ministers in civil partnerships."
l The Unite union said its members at Church administrative headquarters in Edinburgh would take industrial action coinciding with the Assembly over a pay settlement. The Kirk said 29 out of 232 staff voted for action and the event would not be adversely affected.