studentized residuals

I am running five simple linear regression models with the same independent variable but I vary the dependent variable. Our sample size is $n=23.$ We want to test for outliers to see if our $R^2$ would increase (it's actually the reviewer who asked us). The independent variable is log-distance from an industry so outliers on $X$ are really part of our study design. $Y$ is log-concentration of different contaminants. We ran studentised residuals and I am hesitating on what cutoff, but I was thinking of using a cutoff of ${\sim}2$ in $3/5$ models. Is that a reasonable choice? Do u think $2/5$ models would be ok also? (There were no influential values using Cook's distance${}>1$ and DFFITS $\left(\text{threshold 3} \cdot \sqrt{p_\text{prime} / (n - p_\text{prime})}\right)$.)