You can do this using a "generalized formula." The intuition here is to use the following formula for observed agreement, which uses the number of raters rather than conditionals for specific raters.
$$p_o=\frac{1}{n'}\sum_{i=1}^{n'}\sum_{k=1}^q\frac{r_{ik}(r_{ik}^\star-1)}{r_i(r_i-1)}$$
where $n'$ is the number of items that were coded by two or more raters,
$q$ is the number of possible categories,
$r_{ik}$ is the number of raters that assigned item $i$ to category $k$,
and $r_i$ is the number of raters that assigned item $i$ to any category.
$r_{ik}^\star$ allows you to use a weighting scheme to account for non-nominal categories if desired.
Click the links below to get more information from my website or read Gwet (2014).
Formula and MATLAB function for generalized Cohen's kappa
Formula and MATLAB function for generalized Scott's pi (AKA Fleiss' kappa)
Reference
Gwet, K. L. (2014). Handbook of inter-rater reliability: The definitive guide to measuring the extent of agreement among raters (4th ed.). Gaithersburg, MD: Advanced Analytics.
Uebersax, J. S. (1982). A design-independent method for measuring the reliability of psychiatric diagnosis. Journal of Psychiatric Research, 17(4), 335–342.