Integrated biorefineries offer an efficient way to produce biofuels by enhancing profit through the generation of marketable by-products and by reducing environmental impact by reutilizing waste streams originating from different processes within the system. Employing a variety of conversion technologies, integrated biorefineries yield a wide range of products and byproducts, encompassing biofuels, biochemicals, and bioenergy, all derived from biomass feedstocks. Several mathematical methods have been developed in order to optimize the design of biorefineries with consideration for uncertainty, including the multi-objective target-oriented robust optimization (MOTORO) approach that enables target-seeking behavior while maximizing the tolerable deviation of parameters in the system. However, the phenomenon of heterogenous robustness levels that tradeoff risks with each other has not been investigated in both MOTORO and in wider robust optimization literature. The present study addresses this gap by applying multiple, potentially non-equal degrees of robustness to each customer's demand, allowing stakeholders to place unequal risks on each customer. As a result, limited resources may be more efficiently utilized in line with existing knowledge or preference regarding uncertainties. The proposed improvement was applied to an algal biorefinery system with two customers, where robustness successfully exhibited tradeoffs with each other while retaining inverse relationships with system underperformance and variation as evaluated from a Monte Carlo simulation.