Policy Letter faces five amendments, but deputies urged to ensure it is prioritised and finished this States sitting.
There appears to be little common ground between the Education Committee and Guernsey's three private colleges aside from both wanting debate to be concluded, one way or another, before the end of the mid March sitting.
Both sides remain where they were when the policy letter, that could see £2.8M per year of government grants to Ladies, Elizabeth College and Blanchelande phased out, was published.
Education says the money would be better spent in the States school sector and removing funding will promote educational equality.
The colleges argue that they offer better value per pound spent on educating pupils.
A new amendment, from deputy John Dyke, suggests a bursary or open access scheme. This would see pupils from less well-off backgrounds paid by the States to be educated at one of the colleges. Initially the intake would be around 30, but this could increase.
Funding is estimated at a modest £450,000 per year, increasing to an upper limit of more than £3M after seven years, given maximum numbers on the scheme.
Deputy Heidi Soulsby argues that the original policy letter creates a barrier to collaborative working between the State and private education sectors.
Her amendment suggests that partnership working is most effective when government stands aside and senior figures from the private and state education sectors forge links.
It has the backing of the three colleges, as does the St Pier and Ferbrache amendment, which would see States funding decrease if pupil numbers dip.
The colleges and Education have appealed to deputies to finish the debate by 21 March as the deadline nears for setting their new fees.
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