CPT-Europe-4x A3-AGP-Asia can certainly be done though it almost certainly requires multiple bookings to pull off. Getting to 24k miles is also doable but it depends on the earning rates of the airlines you fly and the booking class of the fares. The rule of thumb is that the cheapest paid fares won't earn tier miles in Europe (often in Asia as well), and the next more expensive only earn a few. CPT to Europe and Europe to Asia (and I presume Asia-CPT) have opportunities to earn tier miles on "relatively" inexpensive tickets, though. 4x A3 will earn a few thousand tier miles, or several thousand if you spend more on the fares.

AGP has nonstop service to several European cities on *A airlines. Most of them are Lufthansa group, but also SAS and TK. All of them are notorious for low/no accrual on cheap fares. These airlines also offer nonstops from many cities to BKK, making AGP-[city]-BKK on a single ticket possible.

Thai offers ARN/CPH/FRA/MUC/ZRH-BKK-TPE; those European cities all have nonstops from AGP on Lufthansa group or SAS. Thai earns miles much better than nearly all other *A partners, though some people are wary of flying them...their service standards are reported to have declined from previous. EVA offers AMS-BKK-TPE, with higher reported service standards and much lower earning rates; AMS does NOT have nonstop *A service from AGP.

Getting between CPT and Europe generally means fewer miles than you might expect. The exception is if you fly Ethiopian and connect in ADD; Ethiopian is another stellar earning carrier. The airline itself is solid, but the broader situation in Ethiopia (and bordering countries) would make me carefully consider flying with them.

My personal choice, not knowing your schedule or preferences, would be CPT-IST on Turkish; IST-ATH-short RT in Greece-IST on A3 to get the 4x (probably an overnight in ATH due to schedules); IST-AGP on Turkish; AGP-ARN/CPH/FRA/MUC/ZRH; ARN/CPH/FRA/MUC/ZRH-BKK-TPE on Thai. That plus a presumed return to CPT should put you within striking distance of 24k, especially if you don't go with the cheapest options.