Given that resource providers and consumers may have different requirements and performance goals, concurrent negotiation is considered in this work to successfully obtain commitments with multiple resource providers for consumers in Grid. This work devises a concurrent negotiation mechanism for Grid consumers to acquire multiple resources in which both consumers and providers can renege on contracts. The novel contribution of this work is devising a concurrent mechanism that coordinates multiple one-to-many concurrent negotiations using a regression-based coordination strategy. Empirical results show that the regression-based coordination strategy is stable for different number of required resources and outperformed existing coordination strategies in terms of utility in different kinds of resource market.