Plant Growth has this effect as an option:
Enrichment: This effect targets plants within a range of a half-mile, raising their potential productivity over the course of the next year to one-third above normal.
Can you use plant growth three times in order to double the yield?
You cite what the spell does:
Enrichment: This effect targets plants within a range of a half-mile, raising their potential productivity over the course of the next year to one-third above normal.
It raises the productivity to one-third above normal, not above the current level of productivity. So, no matter how many times you cast it, it will always only raise it to one third above normal.
The spellcasting rules also have this rule
Two or more spells with instantaneous durations work cumulatively when they affect the same target.
If you think that the increased productivity would be normal, because the spell creates an instantaneous effect, and therefore leaves no ongoing magical effect behind, then you could combine them in the way you envision. By this logic you could however create plants that produce hundreds or thousands1 of times the normal amount if you cast the spell often enough, and still consider it normal. To me, that is an absurd interpretation of the term, and working back from there, I think that the magically boosted productivity, even though not magical any more, is not normal any more, either.
1 Like in the old story with the wheat corn being doubled for every field of a chess board, this exponential growth would get you to over a 1000-fold productivity with just 25 castings.