This research addresses the process of task allocation in a heterogeneous multi-agent fleet through the introduction of a novel mechanism in existing decentralised consensus algorithms: bid intercession. Bid intercession refers to the principle of agents biding on behalf of other agents in decision-making architectures leveraging market-based decision strategies. The method exploits and extends existing consensus-based allocation processes through the redistribution of responsibilities in the auction process to achieve various degrees of centralisation in the task allocation process. It is demonstrated that the extension proposed allows for hybridising multiple allocation methods together and structuring the auction process (notably through embedding hierarchies and decision trees directly in the decision-making process) all the while retaining the convergence robustness and performance guarantees provided by the underlying algorithms. The Search and Rescue case study is investigated to assist in framing the research and provide a reference scenario for the application of such concepts. This concept, unexplored so far in consensus-based approaches, not only opens up a sway of coordination architectures and optimisations but also paves the way to novel ethically compliant autonomous systems while retaining essential performance and robustness properties crucial in high-stake applications.