Here are some current or proposed infix operations with three operands. All of these parsings can be specified with a slightly modified BNF. I illustrate with the proposal for the fused operation.

If <fact> is the syntactic category of expressions with with operators of precedence greater than multiply then we have productions:

Where precedence terminology is used to define expression semantics, one can simply say that whenever multiplication operators take precedence over addition operators, the fused multiply add is to be used.