I suppose this might be possible by retraining your own classifier using both 16S and ITS reads. After all, you can train silva to run on both 16S and 18S amplicons. But I think there is a more elegant and arguably more defensible option: process them separately, then merge your OTU tables.
qiime feature-table merge \
--i-tables table-1.qza \
--i-tables table-2.qza \
Warning! This only works if all your OTUs have different names. You wouldn’t want 16S OTU_1 and ITS OTU_1 to be added together! So after you merge, do a quick
qiime feature-table summarize to make sure that all your OTUs from both data sets are present and combined number of OTUs didn’t go down after the merge.
While I’m mentioning this, you might want to think about methods for normalizing between the two different amplicon types (but that might not be a big issue if all your changes are relative ).
Let me know what method you want to try.