Thanks for the suggestion @swbarnes2. After checking out the cellranger aggr webpage, I found the following which was very informative:
cellranger aggr is not designed for combining multiple sequencing runs of the same GEM Well. For that, you should pass a list of FASTQ files from multiple sequencing runs of the same GEM well to the --fastqs argument of cellranger count.
So I'll give that a go and we'll see what happens.
It would be useful to add if the runs were done on same chemistry/sequencer type or different. e.g. both runs were on NovaSeq or were they run on two different types of sequencers e.g. NextSeq and HiSeq.
Thanks for the note. To clarify, both of these were run on a NovaSeq. However, they were run at different universities across the US.