Is it possible to merge scRNAseq data from experiments with different design?
It’s right there on the cellranger manual:

#aggregate results of counts for separate samples
cellranger aggr
#analyse the combined results
cellranger reanalyze


Note: I’m not sure this applies to the above case where batch effects could be an issue. However, this is how the analysis is performed for 10X data from multiple runs in principle.

cellranger aggr

cellranger reanalyze