how to cache a subset for cascading select queries in mysql
If filter 110M is exactly a subset of filter 126M, then appending more AND with WHERE would have done the job.

$sql1 = "SELECT ..... WHERE ...";
$sql2 =  $sql1 . "AND column-name  = ....";
$sql3 =  $sql2 . "AND column-name  = ....";


If that is complex to accomplish try to CREATE VIEW of the previous SELECT statement and the next SELECT statement should query from the view.