The article introduces a new model called cooperative games with overlapping coalitions (OCF games) to deal with situations where agents can be part of multiple tasks. The researchers explore stability in this setting by defining a core that maximizes social welfare. They also introduce balancedness for overlapping coalitional games and show that convex games have a non-empty core. Alternative notions of stability in OCF games are proposed, and their relationships with traditional core concepts are examined. The study provides insights into the fundamental structure of different core concepts in cooperative games with overlapping coalitions.