Can Souls in Purgatory Intercede for Us?

Whether or not the souls in purgatory can pray for us is an open theological question. The principle of lex orandi, lex credendi (the law of prayer is the law of belief) would seem to argue against it, since the liturgical prayers of the Church never ask the souls in purgatory to pray for us. However, prominent theologians throughout history have been on both sides of the question.

For example, St. Thomas Aquinas argued against it, while St. Alphonsus Liguori argued in favor. The general consensus seems to be that while the souls in purgatory are not normally aware of our prayers, it is still possible that God at times reveals to them our prayers and accepts their prayers on our behalf.  However, because their state is such that they are in great need of our prayers, the Church commends us to pray on their behalf rather than implore their intercession.