As a greeting in parting you often say "Take care" (at least in the US, I am not so sure about the UK).
Can you also say "Take you care" or answer with "Take you care, too"?
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(You) Take care.
I have no idea what your native tongue is. But you might be interested in the subject of word order. If you find yourself switching the order of words in a sentence (usually because you are mentally translating on the fly), then it is very likely because your native language follows a word order different from English.
"Take care" is in the imperative, i.e. it is a command or request. "You" is assumed as the subject and not normally included. This is the same for all imperatives. "Sit down", "Pass the salt", "Bring a friend", etc., you do not include an explicit subject except in rare cases where it is needed for clarity or emphasis.
The simple answer is "No" you cannot say "Take you care" in any context.
In this context, "You" is implied because the construction is an imperative, and modern English does not compose 'you' in the ways of Middle English. The correct for, is "Take care of yourself" since the subject is now explicit.
"You take care" is an imperative (order-instruction) that can gain tremendous (and socially awkward) force through inflection.
Colloquially, "take you care" is an expression I have most-often heard used in the 'middle US' states. I feel that moving the "you" to from the beginning to the middle of the expression does the action of 'softening', and thus personalizing (de-formalize), the culturally-uncouth nature of an imperative construction. Like most colloquial expressions, users are likely to bond more with speaker.