I have two data set that were sequenced on Illumina Miseq, however, one was sequenced targeting V3 and the other with V4. Would it be possible to analyze the two data sets together?
The answer is “maybe” and there are a lot of things to think about here. What specifically are your primers? What is your research question? How do you want to combine them?
I think in general, you will have a bias in your data from the primers (see Figure 1 from this paper). But, you might be able to swing something.