Time-lapse seismic monitoring aims at resolving changes in a producing reservoir from changes in the reflection response. When the changes in the reservoir are very small, the changes in the seismic response can become too small to be reliably detected. In theory, multiple reflections can be used to improve the detectability of traveltime changes: a wave that propagates several times down and up through a reservoir layer will undergo a larger time shift due to reservoir changes than a primary reflection. Since we are interested in monitoring very local changes (usually in a thin reservoir layer), it would be advantageous if we could identify the reservoir-related internal multiples in the complex reflection response of the entire subsurface. We introduce a Marchenko-based method to isolate these multiples from the complete reflection response and illustrate the potential of this method with numerical examples.