If some phonological process (like gemination from here) happens only at morpheme boundary (say, only in the coda of a syllable when a certain suffix is added to the stem whose final syllable is that syllable), is there a way to express this in the SPE notation? Or do just people say "this rule applies only at morpheme boundary" (or something like that)? Or if not, is there any standard way to express such things?
In common SPE-style notation,
# is used for word boundaries, and
+ for formative (i.e. morpheme) boundaries. (Sometimes these are treated as special not-segments that have features but are [–segmental].)
So to express something happening only at a morpheme boundary, you could say, for example:
C → [+geminate] / _ + V
That is, "a consonant becomes [+geminate] when it appears before a vowel at a morpheme boundary".
As far as I'm aware, morpheme boundaries were indicated in SPE by a large + symbol. The standard way to address the type of phenomenon you describe was a combination of boundary erasure and the cycle. The basic idea is that all rules apply on one cycle, then (some) boundaries are erased, and then all rules apply on the next cycle, etc. This allows for distinguishing different kinds of morpheme, some of which trigger phonological rules and some of which do not. Cyclicity has survived in general in Rule-Based Phonology (post-SPE phonology), but I'm not up on the latest formalisms used.
"SPE notation" is a superset of SPE theory, that is, SPE theory makes certain claims, many of which are reduced to notational conventions, but the notation transcends that specific theory, and is still used even in OT analyses. The symbol "+" was introduced into linguistic practice well before SPE as a means of indicating the boundaries between morphemes and has been so used for a long time. It is a long-standing practice that grammatical statements are often expressed in ordinary English, even when it is possible to write them in standard notation.
"Only at morpheme boundaries" gained a certain special status in SPE theory because they posited a general convention that in a rule applying in the context "_ZYX", that rule string was interpreted as meaning "_Z+YX", "_Z+Y+X", "_ZY+X" and "_ZYX", that is, with a morpheme boundary optionally present between any two matrices. Explicit mention of morpheme boundaries then means "only when a morpheme boundary is present in that position".