Countifs Multiple Criteria

One way would be to add a helper column which returns 1 for each row if any of the relevant values equal 1. Then a simple SUM formula can sum up the 1s and 0s in that helper column. The helper column formula would be something like this, copied down the column:

=AND(D2="abc",OR(AO2=1,AS2=1))+0

Another option would be to adapt your COUNTIFS formula like this:

=COUNTIFS(ccs_export!$D:$D,"abc",ccs_export!$AO:$AO,1)
    +COUNTIFS(ccs_export!$D:$D,"abc",ccs_export!$AS:$AS,1)
    -COUNTIFS(ccs_export!$D:$D,"abc",ccs_export!$AO:$AO,1,ccs_export!$AS:$AS,1)

This option would not be practical for the potential combinations of 15 COUNTIFS() functions.

Another option would be to use SUMPRODUCT.

=SUMPRODUCT(--(ccs_export!$D:$D="abc"),--(((ccs_export!$AO:$AO=1)+(ccs_export!$AS:$AS=1))>0))

If you go for the SUMPRODUCT option, try not to use whole column references because it will slow your workbook down.