This paper introduces Interactive Tables (iTBLS), a dataset of interactive conversations situated in tables from scientific articles. This dataset is designed to facilitate human-AI collaborative problem-solving through AI-powered multi-task tabular capabilities. In contrast to prior work that models interactions as factoid QA or procedure synthesis, iTBLS broadens the scope of interactions to include mathematical reasoning, natural language manipulation, and expansion of existing tables from natural language conversation by delineating interactions into one of three tasks: interpretation, modification, or generation. Additionally, the paper presents a suite of baseline approaches to iTBLS, utilizing zero-shot prompting and parameter-efficient fine-tuning for different computing situations. We also introduce a novel multi-step approach and show how it can be leveraged in conjunction with parameter-efficient fine-tuning to achieve the state-of-the-art on iTBLS; outperforming standard parameter-efficient fine-tuning by up to 15% on interpretation, 18% on modification, and 38% on generation.