The process of satisfying daily demands is a fundamental aspect of humans' daily lives. With the advancement of embodied AI, robots are increasingly capable of satisfying human demands. Demand-driven navigation (DDN) is a task in which an agent must locate an object to satisfy a specified demand instruction, such as ``I am thirsty.'' The previous study typically assumes that each demand instruction requires only one object to be fulfilled and does not consider individual preferences. However, the realistic human demand may involve multiple objects. In this paper, we introduce the Multi-object Demand-driven Navigation (MO-DDN) benchmark, which addresses these nuanced aspects, including multi-object search and personal preferences, thus making the MO-DDN task more reflective of real-life scenarios compared to DDN. Building upon previous work, we employ the concept of ``attribute'' to tackle this new task. However, instead of solely relying on attribute features in an end-to-end manner like DDN, we propose a modular method that involves constructing a coarse-to-fine attribute-based exploration agent (C2FAgent). Our experimental results illustrate that this coarse-to-fine exploration strategy capitalizes on the advantages of attributes at various decision-making levels, resulting in superior performance compared to baseline methods. Code and video can be found at https://sites.google.com/view/moddn.