The talks on Thursday come six months after the last effort which failed due to differences over voting rights.
Ahead of the meeting, the EU’s Irish presidency put forward a compromise package on contentious issues.
But even lesser matters have caused significant debate, especially over the necessity of mentioning Europe’s Christian heritage in the document’s preamble.
Newer issues will include nominating a replacement for the outgoing European Commission President Romano Prodi.
Several names have been suggested – including the current prime ministers of Belgium, Ireland and Luxembourg – but Prodi has said there is no obvious successor to him.
At the December summit in Brussels, Poland and Spain blocked the agreement because they would have lost gains secured in previous agreements.
To meet their concerns, the EU’s presidency proposes to modify the so-called double-majority principle which determines how EU decisions are made.
Belgian PM Guy Verhofstadt is
Instead of requiring the support of 50% of member states making 60% of the EU population, the new draft sets the figures at 55%-65%.
Other changes may include whether to trim down the European Commission from the expected 25 members to 18, but only from 2014.
However, debate may be more heated over a proposal to agree a minimum of six seats per country in the European Parliament – a move aimed at placating smaller EU nations who fear their voice will be lost in the 732-seat assembly.