This needs some work but can be achieved using scenarios and partitioning.
You would have your "stock" dataset (not partitioned), and a changes dataset, partitioned by day. You will need to create a coding recipe that takes the change dataset both at input and output, but with a partition dependency that says
"to compute day N of the change dataset, I use the stock dataset and day N-1 of the change dataset" (use the "Time range" dependency)
Then your recipe does the actual computation
An important point is that you should not run this recipe in "recursive" mode, because this would recurse until the big bang (since to compute day N-1, you need day N-2 which needs day N-3, ...)
Then this can be automated using a time-based trigger, since you expect your files to change daily (note that this requires a professional version of DSS)