Due to the significant strides made in renewable energy generating units, they are now an appealing choice for supplying energy with various benefits. Furthermore, the aggregation of different energy generators and resources and the rise of energy conversion facilities, like combined heat and power (CHP), have paved the way for a new category of multi-energy prosumers. This research presents an innovative model for a local energy market structure consisting of an aggregator, prosumers, electricity, gas, and heat utility grids, and consumers. The interplay between these entities is handled as an auction model with proposed bidding strategies in which each player participates to maximize their own objective function. The numerical analysis reveals the impact of the pricing strategy on the prosumers' willingness to provide more energy during peak demand periods. Furthermore, the study highlights the potential for mutually beneficial collaborations between prosumers, which leads to reduced energy costs.