TCASII INDUCED LTSS. ACR X TCASII RA WITH Y HAD LTSS WITH Z.

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ACR X AT FL240 10 E OF DJB; PROCEEDING WBOUND ON AN INBOUND COURSE TO DTW. Y; A PA46; WAS EBOUND 2 MI E OF DJB; AT FL230. CTLR ISSUED FL230 TFC AT 12 O'CLOCK AND 6 MI TO X. X ADVISED CTLR THAT HE HAD THE TFC ON TCASII. SECONDS LATER; AS X PASSED OVER THE TOP OF Y; X MADE A QUICK CLB TO FL260; AND THEN ADVISED THE CTLR OF A TCASII RESOLUTION. THE PLT STATED THAT THE TCASII HAD SPOTTED TFC 600 FT BELOW. THROUGHOUT THE RESOLUTION; Y SHOWED LEVEL AT FL230. AT THE TIME OF THE RESOLUTION; ACFT Z WAS W OF DBJ; AND CLRED TO FL250; PROCEEDING EBOUND INBOUND TO PIT. ACFT X TCASII RESOLUTION PLACED IT IN DIRECT CONFLICT WITH ACFT Z. AN ADJACENT RADAR CTLR QUICKLY CLBED ACFT Z BACK UP TO AVOID HEAD-ON COLLISION. ACFT X TOLD TO EXPEDITE DSCNT BACK TO FL240 TO MAINTAIN SEPARATION WITH ACFT Z. IT APPEARED THE 2 ACFT WERE WITHIN 1000 FT VERTLY; ALTHOUGH I AM NOT SURE. I ASKED X WHAT HE HAD CLBED FOR; AND HE SAID IT WAS FOR TFC 600 FT BELOW. I TOLD HIM AGAIN ABOUT THE FL230 TFC THAT WAS LEVEL; AND HE INSISTED AGAIN HE HAD TFC WITHIN 600 FT BELOW. THERE WAS NO OTHER TFC BELOW HIM AT THE TIME. HE DID NOT EXPLAIN WHY IT TOOK A 2000 FT CLB TO RESOLVE THIS APPARENT PROB. SUPPLEMENTAL INFO FROM ACN 268035: WHEN Z WAS SHOWING FL260 I NOTICED X MADE C INDICATE A CLB TO FL245. IMMEDIATELY I AMENDED X TO FL260. HE HAD GONE THROUGH IT BUT CLBED BACK UP. SECONDS LATER X INDICATED FL260 AND HEAD-ON WITH Z. I THEN CLBED Z TOP FL270 AND CALLED THE LOW ALT CTLR TO TRY AND GET HIM TO PUSH X BACK DOWN. X RESPONDED TO A TCASII ALERT FROM A PA46 WHICH WAS LEVEL AT FL230. THE PA46 TFC WAS ISSUED TO X PRIOR TO THE RA.