This paper investigates utility maximising bidding heuristics for agents that participate in multiple heterogeneous auctions, in which the auction format and the starting and closing times can be different. Our strategy allows an agent to procure one or more items and to participate in any number of auctions. For this case, forming an optimal bidding strategy by global utility maximisation is computationally intractable, and so we develop two-stage heuristics that first provide reasonable bidding thresholds with simple strategies before deciding which auctions to participate in. The proposed approach leads to an average gain of at least 24% in agent utility over commonly used benchmarks.