Building on recent advancements in transformer-based approaches for domestic robots performing 'knolling'—the art of organizing scattered items into neat arrangements—this paper introduces Knolling bot 2.0. Recognizing the challenges posed by piles of objects or items situated closely together, this upgraded system incorporates a self-supervised graspability estimation model. If objects are deemed ungraspable, an additional behavior will be executed to separate the objects before knolling the table. By integrating this grasp prediction mechanism with existing visual perception and transformer-based knolling models, an advanced system capable of decluttering and organizing even more complex and densely populated table settings is demonstrated. Experimental evaluations demonstrate the effectiveness of this module, yielding a graspability prediction accuracy of 95.7%.