Since computationally intensive applications may often require more resources than a single computing machine can provide in one administrative domain, bolstering resource co-allocation is essential for realizing the Grid vision. Given that resource providers and consumers may have different requirements and performance goals, successfully obtaining commitments through concurrent negotiations with multiple resource providers to simultaneously access several resources is a very challenging task for consumers. The novel contribution of this work is devising a concurrent mechanism that (i) coordinates multiple one-to-many concurrent negotiations between a consumer and multiple resource providers, and (ii) manages (de-)commitment for consumers during the one-to-many negotiation in Grid co-allocation. In this work, a utility-oriented coordination strategy and three classes of commitment strategies for concurrent negotiation are presented. A series of simulations were carried out in a variety of settings and favorable results show that the strategies (both commitment strategies and the coordination strategy) outperformed existing models in terms of utility, negotiation speed, and success rate.