BE40 FLC OVERSPD AND OVERSHOOT ASSIGNED ALT CONFLICTING WITH A C21 UNDER LIT DEP CTL.

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COOL CLR DAY; INEXPERIENCED COPLT; PF; L SEAT TO GAIN TIME FOR UPGRADE; CAPT PNF (PIC) FLYING R SEAT. ON TKOF FROM LIT RWY 4L; RWY HEADING TO 4000 FT; CLBING THROUGH 2000 FT MSL WITH A HIGH PWR SETTING; ATC GAVE HEADING CHANGE TO 330 DEGS; ADVISING OF TFC AT OUR 10 O'CLOCK POS MOVING TO 12 O'CLOCK POS IN THE TURN. PNF WAS COMPLETING THE AFTER TKOF CHKLIST AND BEGAN SEARCHING FOR THE TFC. PF MADE REMARK ABOUT GOING FAST; THEN TCASII BEGAN RA SERIES CALLS OF TFC; CLB AND INDICATED A REQUIRED CLB OF 4900 FPM. AS WE ROLLED OUT ON 330 DEG HDG; PNF SAW C21 TFC (5000 FT MSL) ON R TO L COURSE GOING DIRECTLY THROUGH OUR COURSE; ABOVE US. AS PNF RETURNED ATTN INSIDE THE COCKPIT; WE WERE OVER 300 FT ABOVE ASSIGNED ALT AT 260 KIAS. ATC ADVISED US TO STOP SQUAWK; AS WE INDICATED IN EXCESS OF 300 FT ABOVE ASSIGNED ALT. PWR WAS REDUCED AND DSCNT TO ASSIGNED ALT COMPLETED. THEN ATC ADVISED MODE C SHOWED OUR ASSIGNED ALT. FACTORS: 1) INEXPERIENCED COPLT AS PF IN L SEAT. 2) CAPT PNF IN R SEAT. 3) ATC VECTOR DIRECTLY INTO OTHER ACFT. 4) TCASII RA ADVISING 'CLB;' 'MONITOR VERT SPD' ADDING TO ISSUES IN COCKPIT; ALONG WITH OVERSPD WARNING HORN; THEN LNDG GEAR HORN UPON PWR REDUCTION. ISSUES: 1) ALTHOUGH PF IS FAMILIAR WITH LITTLE ROCK FLYING AREA; THE ACFT IS NEW TO HIM. 2) A HIGH PWR SETTING CAUSED EXCESSIVE SPD AND HIGH RATES OF CLB; PERHAPS CAUSING THE TCASII TO ISSUE AN RA OF CLBING AT 4900 FT TO AVOID THE TFC. 3) ALTHOUGH THE TCASII DIRECTED A CLB; WE IGNORED THAT INPUT TO LEVEL AT ASSIGNED ALT; EXACTLY WHAT WE ARE TOLD NOT TO DO. HOWEVER; A CLB IN THIS CASE WOULD HAVE RESULTED IN AN INTERCEPT AND MIDAIR COLLISION. TCASII RA WAS DISCUSSED AND OVERRULED. RESOLUTIONS: 1) PIC/PNF WILL ADDRESS TCASII CIRCUMSTANCES AND ISSUES WITH THE TCASII MANUFACTURER; AND DEBRIEF PLTS AT THE WORK PLACE. 2) PNF AND PF HAVE DISCUSSED THE CIRCUMSTANCES OF EVENTS LEADING UP TO THE CONFLICT (HIGH PWR SETTING/SPD/ASCENT). 3) PIC/PNF/CAPT WILL TIGHTEN UP PERSONAL LIMITS OF DEVS FROM THE 'NORM' BEFORE DIRECTING/TAKING ACTION.