A common way to intensify a phrase in Latin is to place an intensifier on its verb. An intensifier is a prefix, often a preposition or some other adverb, placed on the verb which can intensify it.
In English, we use intensifiers all the time, but they usually follow the verb. For instance, the verb "tear" (rend or rip) can be intensified by saying "tear up". You have to use some care with intensifiers, because they can also be used to completely change the meaning of a verb. For instance, "take up" is not simply an intensifier of "take", but a whole new verb.
Back to Latin. Carpo has several attested prefixed forms: concerpo, decerpo, discerpo, excerpo, and praecerpo. All of these forms are at least somewhat intensified, although they all introduce some change in meaning or at least emphasis in carpo, so you'd have to excercize some judgment in which of the five you'd care to pick.
If you don't care for any of the attested forms, you might want to coin a new one. I can't help but think of succerpe diem, (grab the day from underneath, from sub+carpo). It reminds me of a not-very-polite and mildly obscene idiom in English (Grab it by the b-lls!), which is, however, quite emphatic.