Consider doing a monthly or quarterly "Bring a Friend Sunday" in order to have an explicit shallow-entry liturgy where parishioners are encouraged to invite their neighbors, friends, and fallen-away Catholics to Mass with them. Ensure that hymns, homilies and worship aids are geared toward or sensitive to those who are disengaged. Consider having some sort of follow-up or hospitality to engage newcomers in conversation and invite them to another shallow entry event.