FLT CREW OF B757 CLBS ABOVE CLRED ALT AFTER RECEIVING MULTIPLE COCKPIT AURAL WARNINGS SIMULTANEOUSLY WITH AMENDED ALT CLRNC; ALT ALERT; AND TCASII TA.

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DEPARTING LGA. TALKING TO ZNY. CLRED TO CLB TO FL280. PASSING FL260; SEVERAL CRITICAL THINGS ALL OCCURRED SIMULTANEOUSLY: ATC AMENDED ASSIGNED ALT TO FL270. FLT ATTENDANTS ATTEMPTED TO GET OUR ATTN (DUE TO INTERMITTENT PROBS WITH THE INTERPHONE SYS) BY GAINING UNANNOUNCED ACCESS THROUGH OUR SECURED 'ENHANCED COCKPIT DOOR;' THUS CAUSING THE AURAL WARNING TO SOUND. THE ALT WARNING CHIMED; BECAUSE THE AUTOPLT FAILED TO CAPTURE FL270; AND HAD ASCENDED TO FL274; AT WHICH TIME THE FO DISENGAGED THE AUTOPLT AND MANUALLY DSNDED TO FL270. COINCIDENTAL TCASII TA FOR TFC APPROX 1000 FT ABOVE AND 2 MI LATERAL. OUR ATTN WAS FOCUSED PRIMARILY ON A PERCEIVED/SUSPECTED UNAUTH COCKPIT ACCESS ATTEMPT. (DEPARTING NYC UNDER AN 'ORANGE THREAT LEVEL.') SUPPLEMENTAL 579370: AS FO; SET FL270 IN ALT ALERT WINDOW; BOTH TCASII ALERT AND ENHANCED COCKPIT DOOR AURAL ALERT SOUNDED. FO SELECTED 'DENY' POS ON THE FLT DECK DOOR CTL PANEL AND LOOKED FOR TFC WHILE CAPT ATTEMPTED TO ESTABLISH COMS WITH THE FLT ATTENDANTS. THE FO SIGHTED TFC AND NOTICED AUTOPLT FAILED TO CAPTURE FL270. CLB WAS STOPPED AT FL274 AND RETURNED TO FL270.