What is the plural of syntax? Would it be syntacies? What rule would govern this kind of construction?
As FumbleFingers has commented, the plural is syntaxes.
That's probably because the normal plural -es is added to the root word, or it may possibly be because the Greek/Late Latin word from which syntax is derived is syntaxis and Greek words ending in -is are pluralised with -es.
If we were to create a spoof plural for syntax it would be syntaces (words ending -x get -ces; the preceding vowel can change as in index/indices). But no-one uses that, or would know what it meant.
An erroneous plural, which I offer for comparison is:
It has a rough comparability in frequency to the less exotic, more naturally English sounding 'syntaxes'.
This is erroneous as a plural of 'syntax' because it is a linguistic term having to do with rule based things but it is not a word to describe a multiplicity of a collection of rules. 'Syntagma' is a sequence of words that form a syntactic unit (for example, a noun phrase), a -single- syntactic constituent (no rule or rules, the plurality is in the (expected) number of words).
Note: I have no explanation whatsoever of the shifted character of the graphs.