It is not clear from your post what you want to accomplish. A multimodal network is a dataset that combines different modes of travel such as rail, bus, bike, pedestrian and car. It has nothing to do with closest facility. Once you have a network on which you want to travel on, you create a closest facility layer and load in your facilities and incidents and solve to compute the distances between them. So if I uderstand your question, you want to compute distances from facilities set X and set Y, then load them into the closest facility layer and solve. If you want to find the distance between one X and one Y then use the Route solver.
Jay Sandhu