The dimensional overlap (DO) theory categorizes various stimulus-response compatible effects (e.g., the manual Stroop, Simon, and SNARC effects) into two main types: stimulus-stimulus (S-S) and stimulus-response (S-R) dimensional overlap effects. The S-S type effect (e.g., the manual Stroop) occurs in the semantic-representation stage, while the S-R type effect (e.g., Simon) occurs in the response-selection stage. However, the processing stage of the SNARC effect, which is also categorized as an S-R type, remains controversial. To investigate this issue, we adopted a modified numeral parity judgment task that could simultaneously induce manual Stroop, Simon, and SNARC effects. According to the additive-factor logic, two effects occur in the same processing stage if they are interactive. In our task, we checked the interaction among the three effects to identify the locus of the SNARC effect. In two experiments with different target numbers (exp1: 1, 2, 7, 8; exp2: 0, 1, 2, 3, 6, 7, 8, 9), the manual Stroop, Simon, and SNARC effects were all observed, showing longer response times and higher error rates in the incongruent conditions than in the congruent conditions. Most importantly, only the interaction between SNARC and Simon effects was observed in the two experiments. This result suggests that the SNARC effect, as an S-R type effect like the Simon effect, occurs in the response-selection stage. In addition, the non-interaction of the manual Stroop and Simon effects and the manual Stroop and SNARC effects in our study repeatedly verifies the independence of the S-S and S-R effects. Our results further support the classification of the DO theory.