How often do wives give birth to more than three children?

Not very often. 

More than 3, ie Quadruplets, Quintuplets and more is 0.00872% of pregnancies.

( Wikipedia says these are the conceptions, it doesn't say whether the women are wives or what percentage of conceptions lead to births. Since some women cull supernumerary offspring to avoid a difficult birth which often leads to death. )

The global average number of children per family is 2.6, so not quite even three kids. But clearly this is an aggregate of some countries with very low birthrates and some countries with very high birthrates. So very rare to see a family that large in Europe but very common to see a far larger family in subsaharan Africa. 

Are you asking about all at once (quadruplets, quintuplets, etc.)? The generally accepted (and crude) formula is "1:89**n-1" -- in other words, "one out of 89 raised to the power of the number of children minus one"... so that would mean 

quadruplets occur about one out of 700,000 births (1:89**4-1), 

quintuplets occur about one out of 55,000,000 births (1:89**5-1), 

and so forth.

This is your 1,489th reply.  The number of children one has is dependent upon many factors, e.g., cultural influences, degree of responsibility, the level of desire to have many children, and for some, the ability to support and parent them, while for others, not so, though it should be the case.

Access to birth control is a significant factor, as is education for women. With both available, the birth rate goes down considerably, suggesting that women (at least) would prefer to have fewer children, if they have a choice.

In countries where this is not so available, or where the catholic church is predominant, having lots of children prevails. 

In traditional cultures, where poverty and disease or even wars are prevalent, having many children is a form of security for one's old age and an assurance that at least some of the children will survive.

I'm getting off into sociology and anthropology here, so your question should properly be addressed not here, in Families and Relationships, but in Society and Culture. 

And you could easily look up the statistics yourself on the internet for more accurate information.

Unless you wanted some advice? 

probably pretty often, my parents had 4 of us