Root canal re-treatment via drilling a full ceramic crown with casted post and core? (Photo)

On my first molar, the endodontist wants to drill through the ceramic crown (placed in 2011) to do re treatment of root canal (initially done in 2008) cause there is painful abscess there and to investigate if a forth (untreated) root is there. Is drilling through casted post and core feasible? Will this drilling make the crown weaker at the end? Is it better to try to remove the crown as a whole? Is it a good strategy to go on antibiotics and simply wait and see?