We talked about the verbs prendere and riprendere in this lesson.
But in a popular Kimbo commercial for coffee featured on Italian TV, there is a play on words using precisely the verb riprendere, so let’s take a closer look, in order to better appreciate the double meaning.

Ti riprendi? -Sì.

Are you getting a hold of yourself [feeling better]? -Yes.

Me [dialetto romanesco: mi] riprendo un altro caffè.

I'll get a hold of another coffee for myself [I’ll have another coffee].

Captions 8-9, Gigi Proietti - Caffè Kimbo - Spot - Mi riprendo un altro caffè

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Prendere (to take) is the basic verb. The prefix ri- generally means "again," so it's logical for riprendere to mean "to retake," and it often does.

BANNER PLACEHOLDER

Gigi Proietti has lost his memory, and the doctor is trying to hypnotize him into remembering something. When we faint, or we feel bad in some way, hopefully, we then "come to," we get a hold of ourselves, we start feeling better. This is another meaning of riprendere, but this time it's the reflexive form, riprendersi. In a reflexive verb, the direct object and the subject are the same. Mi riprendo (I get myself back).

So when Gigi Proietti says, mi riprendo un altro caffè, the direct object in this sentence is caffè (coffee), not Proietti himself. He uses riprendersi, and conjugates it, mi riprendo. On first glance, it looks just like a reflexive verb, but it's not reflexive, because caffè is the direct object. It does, however, use the same attached particles as reflexive and other pronominal verbs, so it's also called un verbo pronominale (pronominal verb). In this case, though, it is specifically un verbo con uso intensivo, o verbo di affetto (an intensified or personalized verb). Apart from its purpose — to personalize or intensify — we can distinguish it from the reflexive verb because, if omitted, the sentence is still complete. 

This extra personalization is commonly used in Italian speech, as in "I’ll have for myself another cup of coffee." We could omit "for myself" and simply say "I’ll have another cup of coffee." In Italian too, instead of mi riprendo un altro caffè, Proietti could have said, riprendo un altro caffè, without intensifying it, but of course, then there would have been no play on words.

So, here, mi stands for a me stesso (for myself). 

Here's another example. Riprendere, like prendere, is a transitive verb, so we need an object, even if the object is oneself.

Let's say I'm out running. After a sprint...

Riprendo fiato (I catch my breath). Fiato (breath) is the direct object.

If, during a long run, I run out of energy, then maybe I’ll need to rest and drink some water.

Mi prendo una pausa (I take a break for myself). Pausa (break) is the direct object.

Then I start feeling better again and continue the run.

Mi riprendo (I get my energy back). Mi (myself) is the direct object.

Riprendo la corsa  (I take up running again). La corsa (running) is the direct object.

BANNER PLACEHOLDER

In a nutshell:

Verbo transitivo (transitive verb):
Prendere (to take)
Riprendere (to take another, to take again, to continue after an interruption)

Verbo riflessivo (reflexive verb), also verbo pronominale (pronominal verb):
Riprendersi (to start feeling better again)

Verbo intensificato (intensified, personalized verb) also verbo pronominale (pronominal verb): 
Prendersi qualcosa (to take something for oneself)
Riprendersi qualcosa (to take something again for oneself)