Are there instances when you include the serum potassium level when calculating a serum anion gap?

No, I don’t. The problem with the AG, to start with, is there is no accepted normal AG. (8-14) UTD says to find out what is normal for your lab, like that is likely. I just use 10… anyway, then to make it higher by adding k to account for the k that may change it by 1 or 2, makes no sense to me when...

The serum potassium level should be used to calculate the serum anion gap if the laboratory reports the anion gap using the formula (Na⁺ + K⁺) − (Cl⁻ + HCO₃⁻). What matters most is that the formula matches the reference range being used by the laboratory.

Only include it if the laboratory you are using does so. Agree with Dr. @Dr. First Last.

I use 12 as the upper normal for AG if K is not included. Including K would increase the upper normal AG by the normal serum K, around 4 usually.