Q:

Calling a stored procedure from a stored procedure in Cosmos Document DB?

Is it possible to call one stored procedure from another stored procedure with Azure Cosmos DB (document DB)? If so, how?

A:

It's not supported but you can include user defined functions in your queries so with some creativity you can often get what you want. 
The design pattern most people use when they need to call multiple SPROCS is to use a message bus to trigger the later calls. 

