If you're using the Advanced Filter Action, "Filter the list, in place", then the answer is no. Applying this action will automatically clear/toggle Auto Filter off; plus, attempting to toggle Auto Filter back on after applying this action will automatically clear the filtered results.
Alternatively, if you were to use the Advanced Filter Action, "Copy to another location", you could then toggle Auto Filter on for the resulting "Copy to" range afterwards.
Having said that, Advanced Filter can handle advanced criteria on its own, including multiple fields. There are other methods for filtering by a list of IDs (e.g. using the ISNUMBER-MATCH method as a criteria formula in a single cell), which would be easier to combine with additional criteria for other fields.
Also, with MS365, it's worth looking into the FILTER function, which is just as capable of filtering by multiple criteria for multiple fields.