I see sample code with target += .... everywhere, but when I used this syntax in my custom function, I keep getting parsing error
58: real sumExt;
59: sumExt += 1.0;
Is this possible? that target += is allowed, but not else where?
Correct. Until 2.17.x
target isn't a variable of the usual kind and target += is a specialized statement. As @bgoodri says, it will be avaiablle for all ordinary variables in Stan 2.17 (probably not out for two or three months).