AN LGT ACR CLBED IN RESPONSE TO A TCASII COMMAND. THE ACFT WAS ON THE ILS INBOUND AT EWR.

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WHILE APCHING EWR AT 3000 FT; ON THE ILS TO RWY 4R; ATC CALLED OUT TFC AHEAD AT 2500 FT. THIS TFC WAS DISPLAYED ON TCASII AND ALSO SEEN VISUALLY BY THE PNF. AS WE APCHED THE TFC; THE TCASII DISPLAYED AN RA OF 'MONITOR VERT SPD' AND THE 'CLB.' WE CLBED APPROX 300 FT TO AVOID THE TFC UNTIL THE 'CLR OF CONFLICT' ADVISORY CAME. OUR CLB IN RESPONSE TO TCASII WAS IMMEDIATELY RPTED TO APCH CTL. UPON DSNDING AGAIN; WE INADVERTENTLY DSNDED APPROX 250 FT BELOW 3000 FT. OUR CLRNC HAD BEEN TO 'MAINTAIN 3000 UNTIL ESTABLISHED -- CLRED ILS 4R.' DURING THIS ENTIRE EPISODE WE WERE ON THE LOC BUT STILL BELOW THE GLIDE PATH. AMONG THE DISTRACTIONS CONTRIBUTING TO THIS PROBLEM WERE THE CONFLICTING AND LOUD VOICE WARNINGS OF 'ALT' AND THE TCASII COMMANDS MAKING COM WITH APCH DIFFICULT. SUPPLEMENTAL INFO FROM ACN 223997: I THINK THE FO INADVERTENTLY DSNDED BELOW OUR ASSIGNED ALT FOR SEVERAL REASONS: HE BECAME DISTRACTED BY THE MULTITUDE OF AURAL WARNINGS AND VISUAL INDICATIONS. FOR EXAMPLE; TCASII AURAL WARNINGS INCLUDED 2 DIFFERENT VOICE WARNINGS; WITH THE VISUAL VSI LIGHT INDICATIONS. AT THE SAME TIME; THE ACFT ALTDEV AURAL WARNING WAS SOUNDING; PLUS I WAS TALKING TO ATC AND INSTRUCTING HIM TO FOLLOW THE TCASII INDICATIONS. WHILE RETURNING TO ASSIGNED ALT; I WAS AGAIN INSTRUCTING HIM AND ATC WAS TALKING TO US.