mysqli & nested queries - maybe I'm rusty...

I am putting together an application where we are almost exclusively 
using stored procedures in MySQL because most of the heavy lifting (as 
it should be) is done in the database.

I have exactly one situation where I need to execute a stored procedure 
and while returning the results if I run a across a particular value in 
those results I need to execute another SP to handle. Because I have 
forgotten which combination or store_result, use_result, fetch_row (not 
to mention that fetch row doesn't have the column names in the array, 
just the index) to use I am banging my head against the wall while 
getting the dastardly "2014 Commands out of sync;" error. Can someone 
provide some insight please?

Assume that $mysqli is the connection -

$sql = "CALL sp_ONE(" . $product . "," . $level . ")";
if(!$result = $mysqli->multi_query($sql)) {
     echo "Error: (" . $mysqli->errno . ") " . $mysqli->error . " on 
Query " . $sql;
} else {
     do {
         if($side = $mysqli->store_result()) {

             /* output the list */
             echo '<ul>';
             while($row = $side->fetch_row()) {
                 /* careful, column names aren't carried over */
                 echo '<li data-page="' . $row[2] . '">' . $row[1] . 
'</li>';
                 /* do we need to do a another stored procedure? */
                 if(isset($row[3])) {
                     /* get the info */
                     $sql = "CALL sp_TWO(" . $product . "," . $row[0] . ")";
                     if(!$subResult = $mysqli->multi_query($sql)) {
                         echo "Error: (" . $mysqli->errno . ") " . 
$mysqli->error . " on Query " . $sql;
                     }
                     /* output the extra info */
                     echo '<ul>';
                     while($sub = mysqli_fetch_array($subResult)) {
                         echo '<li data-page="' . $sub[1] . '">' . 
$sub[0] . '</li>';
                     }
                     echo '</ul>';
                 }
             }
             echo '</ul>';
             $side->close();
         }
     } while($mysqli->next_result());
}