Currently the spec for box-shadow (https://drafts.csswg.org/css-backgrounds/#box-shadow) does not appear (to my quick reading) to give any instructions for additive composition (https://drafts.csswg.org/web-animations-1/#effect-composition) when animating.

In the absence of a behavior for addition, the fallback is to use replace (https://drafts.csswg.org/css-values-4/#combining-values).

Firefox instead appears to implement box-shadow interpolation as list concatenation, as shown by https://output.jsbin.com/pikiguv. Chrome appears to do component-wise addition. Which, if either, is correct?

EDIT: Note, you will need composited modes enabled in the browsers if you test them. For Chrome, that's chrome://flags, set "experimental-web-platform-features" to enabled. For Firefox, you can test using Firefox Nightly (has it enabled by default).