Combining stats of multiple BLAST queries

Hi all,

I have a FASTA file with let's say following structure:

>Query_1
actgacgac....>Query_2
gtacgatcagct...

I want to BLAST this FASTA file against a set of databases one by one and combine the results. The combining of alignments in results is a relatively easier task, but I wanted to know if we can combine the individual search statistics too so that the end result is same as if the file has been blasted against all of the databases at once.

I know it might sound stupid to BLAST one by one while we can blast against all databases at once, but I'm just being curious about the algorithm and its intricacies.

Thanks,