A CE560 FLT CREW FLYING THE TEB 5 OUT OF TEB EXPERIENCING HYDRAULIC SYSTEM DIFFICULTIES OVERSHOT CLRNC LIMIT ALT OF 1500 FT BY 160 FT.

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IMMEDIATELY AFTER TAKEOFF FOR TEB ON THE TEB 5 DEP WE INCURRED MULTIPLE SYSTEM FAILURES CLBING OUT OF 1300 FT. THIS INCLUDED AN UNSAFE/IN TRANSIT GEAR WARNING LIGHT; HYDRAULIC PRESSURE LIGHT AND MOST IMPORTANTLY A STABILIZER MISCOMPARE LIGHT. THE PF DID AN EXCELLENT JOB OF FLYING THE AIRPLANE FIRST BUT THE ACFT CLBED TO 1660 FT BEFORE THE CLB COULD BE ARRESTED. I ATTRIBUTE THIS TO THE MULTIPLE AND UNRELATED FAILURES AND CTL INPUT DIFFICULTIES. THE UNDERSTANDABLY ANGRY CTLR POINTED OUT THIS EXCURSION IMMEDIATELY. WE WERE SO BUSY TRYING TO FIGURE OUT WHAT WAS GOING ON; THAT I WAS UNABLE TO ANSWER HIM IMMEDIATELY. WE INSTANTLY RETURNED TO 1500 FT. BUSY ARPT; BUSY DEP; LOTS OF FLASHING LIGHTS; WARNING HORNS; GOING PRETTY FAST AND CLOSE TO THE GND; ALL HAPPENING WITHIN A FEW SECONDS. WHILE I OFFER NO EXCUSE FOR AN ALT BUST; I WILL ADMIT THAT THE DECK WAS STACKED AGAINST US. WE ARE ALL TAUGHT IN SIMULATOR TRAINING THE SCENARIO FOR AN ENGINE FIRE OR FAILURE AFTER TAKEOFF. THIS TRAINING BECOMES SECOND NATURE. SELDOM ARE WE TESTED/TRAINED TO HANDLE A PITCH PROB CLOSE TO THE GND FLYING; SOMETHING MORE THAN A SIMPLE DEP WITH MULTIPLE FAILURES THAT DON'T MAKE ANY SENSE. IN 25 YEARS OF FLYING I HAVE NEVER BEEN SO BUSY AT 1300 FT ABOVE THE GND; IN A HIGH DENSITY TFC AREA; TRYING TO FIGURE OUT WHAT WAS GOING ON. GIVE ME THAT OLD FASHIONED V1 CUT; ENGINE; FAILURE; ANY DAY.