Brazil has been recently visited two seasons ago that looks more wasted being an overused country, so Chile could be the good place to go.
Here's the list of flights to Santiago from Split:
Lufthansa (LH) 1413 to Frankfurt (FRA), departs at 6:40 pm and arrives at 8:25 pm
Lufthansa (LH) 510 to Buenos Aires (EZE), departs at 9:55 pm and arrives at 6:45 pm the next day
Sky Airline (H2) 502 to Santiago (SCL), departs at 9:40 am and arrives at 11:00 am
Lufthansa (LH) 1413 to Frankfurt (FRA), departs at 6:40 pm and arrives at 8:25 pm
Lufthansa (LH) 506 to Sao Paulo (GRU), departs at 10:05 pm and arrives at 4:55 am the next day
LATAM (LA) 8026 to Santiago (SCL), departs at 8:05 am and arrives at 11:30 am
JMO