This paper addresses the question of how current group decision-making systems, including collective intelligence algorithms, might be constrained in ways that prevent them from achieving general problem solving ability. And as a result of those constraints, how some collective issues that pose existential risks such as poverty, the environmental degradation that has linked to climate change, or other sustainable development goals, might not be reliably solvable with current decision-making systems. This paper then addresses the question that assuming specific categories of such existential problems are not currently solvable with any existing group decision-systems, how can decision-systems increase the general problem solving ability of groups so that such issues can reliably be solved? In particular, how might a General Collective Intelligence, defined here to be a system of group decision-making with general problem solving ability, facilitate this increase in group problem-solving ability? The paper then presents some boundary conditions that a framework for modeling general problem solving in groups suggests must be satisfied by any model of General Collective Intelligence. When generalized to apply to all group decision-making, any such constraints on group intelligence, and any such system of General Collective Intelligence capable of removing those constraints, are then applicable to any process that utilizes group problem solving, from design, to manufacturing or any other life-cycle processes of any product or service, or whether research in any field from the arts to the basic sciences. For this reason these questions are important to a wide variety of academic disciplines. And because many of the issues impacted represent existential risks to human civilization, these questions may also be important by to all by definition.