Classical Morse theory connects the topology of a manifold with critical points of a Morse function. Stratified Morse theory considers the topology of a stratified space with critical points of a stratified Morse function. Discrete Morse theory is considered as a combinatorial adaptation of Classical Morse theory, and is applied to simplicial or cell complexes. It seems natural to ask whether there could be a combinatorial adaptation of Stratified Morse theory. This talk will serve as a conversation starter, where I would like to discuss a (possibly) discrete version of stratified Morse theory and its (potential) application in data analysis.