Transport systems are prone to disruptions due to various factors, from extreme weather conditions to public transport failures and road accidents. These disruptions alter travel dynamics and affect expected travel time and cost, prompting passengers to cancel trips, wait for resolution, or change paths and mode. This paper aims to provide a data-driven methodology for gaining insights into how mode choice is affected by disruptions. First, we use multi-source data to form a unified multi-modal dataset of car, public transport, and bike-sharing demand data. Then, by introducing a signature range, we define an hourly range of expected demand. Utilising this signature range, we first detect hours with irregular demand in each mode and then proceed to spot instances where a potential inter-modal demand spillover has occurred. Finally, exploring our data from Lyon, France, we showcase examples of implementing our method to actual recorded data. Our study paves the way for more extensive studies on the inter-modal demand spillover and its management implications.