Q:

Can children learn up to 4 different languages? And how to do it?

An example is parents with different mother tongues living in a foreign country, 
teaching those three languages and also English.
How and when should this language be taught?
Can all be taught in early age or only when the others are firmly embedded?
What languages should be taught first? The similar ones or the local language?

A:

In parts of the world very dense in languages (e.g. Nigeria, India, Papua New Guinea), a common scenario is this: a child's mother speaks language A, the father speaks language B, a vehicular language C is frequently used for interactions between people from different villages, especially in cities, and language D is an official language which is the medium of instruction in government schools. In such places it is not at all uncommon for a young adult to be fluent in four languages.
For concreteness, imagine an Indian child whose mother is Tamil and whose father is Telugu. The child speaks these languages within his/her extended family. Hindi is used when going out into town to do business, and English is used in school. 

A:

Our daughter (29 months old) is currently learning 4 languages. I am a native speaker of Swedish and Greek, while my wife is a native speaker of Turkish. We live in Sweden, so our little one is exposed to Swedish when she's at kindergarden or in contact with relatives. I talk explicitly Greek with her, while her mother speaks only Turkish. Her grandmother speaks only Swedish with her. Me and my wife have been speaking mainly English, so she has snapped up that as well. The result:

She understands all 4 languages
She addresses each one of us explicitly in the language we talk to her.
Grammar works well: a) She uses articles in Greek, b) definite/indefinite in Swedish, c) agglutination works fine in Turkish (i think)
In interaction with locals she uses local words to address us e.g. pappa instead of baba, mamma instead of anne.
She knows how to change language context e.g. you asked her to count in all 4 languages separately and she does that without being confused
She is a late talker, but that is expected. Besides, my friend's monolingual child is a late talker too. 

The most important rule however is one and only: Do not mix up the languages when addressing the child. The language you use to communicate with your child should be your native tongue. If you talk half English, half Spanish at the same time, the child will probably end up not speaking well the language it doesn't hear from its environment. While making a sentence it will be like 5 words in Spanish 3 in English, then 3 Spanish 2 English and so on. 

