By the rules you’d be able to do it with only six TK flights as it only counts the arrival into the continent. However using TK for the return leg might help just transiting through IST each time.
If I tried it, my TK Elite (*A Gold) would be handy. Award tickets don’t count, although the rules are silent on using miles for upgrades once ticketed.
Oceania. IST-SIN-MEL on TK168 is the cheapest for getting to Aus and is considered a ‘single’ flight with the SIN stop just for fuel. $996 ow / $1500 rtn
Africa. IST-SSH (Sharm El-Sheikh, Egypt) $200 ow seems about cheapest and easiest. But at $550 rtn maybe better value using a different airline to get back to IST.
Asia. The Middle East is considered Asia so IST-KWI (Kuwait) seems cheapest there at $180 ow. Same day return seems expensive but only $300 if overnight in Kuwait.
Europe. IST-PRN (Pristina, Kosovo) can be had for $55ow, but $255 for same day return.
North America. IST-YUL (Montreal, Canada) seems cheapest for $527ow. Return on TK is $1060 but requires two nights stay.
South America is the dearest one way trip at $1550ow IST-GRU (Sao Paolo, Brazilian), but return can be had for $1830.
That would be about $5500, using TK return flights in whY. Maybe cheaper if you used an LCC for the flight back to IST but then you’d need a visa each time entering Türkiye.
You’d also need about 12 days to do it.
