At this stage the following actions may be considered:
Coordinate the presentation and submission of an amicus curiae (interested party) brief to the court. Some jurisdictions only allow an amicus to be included upon submission of the complaint and not subsequently.
Facilitate contact between reporters and lawyers assigned to the case from the court, commission or committee.
Depending on the forum, stay in frequent contact about your case, particularly if it has stalled.
Consider organizing a thematic hearing. You can watch one held in 2013 at the Inter-American Commission for Human Rights by Asylum Access and other parties seeking a review of RSD processes in the Americas.