Approaches to creating composite data lists from multiple RESTful sources

Hope this question isn't too high level. I'm working on an Android Application at the moment that connects to the Spotify Web API (using Retrofit), the end result is a list of tracks which is generated from data collected from other API calls, for example a users top tracks, top artists etc... Because the end result I need is constructed from a few different API calls I'm concerned the logic is a bit messy, at the moment it's essentially:

getFirstBitofRequiredData -> onDataReady -> getNextBitofData ->      OnDataReady -> getMoreData(combinedDataSets) -> onDataReady -> createDataModelObjectsForView(moreCombinedDataSets)

Something to that effect anyway! I was wondering is there any specific architectural approaches to implementing this kind of sequential and combinational method of getting data?

Thanks in advance,

Garry