Do any sects permit consensual open marriages? 1 Corinthians 7:4 says:


  The wife does not have authority over her own body but yields it to her husband. In the same way, the husband does not have authority over his own body but yields it to his wife.


If a man sleeps with another woman without his wife's knowledge or consent, that would be adultery. But what if he does so at the behest of his wife, with her knowledge and consent, even instigation, as Abraham did with Hagar at Sarah's suggestion? Is he then relinquishing "authority" over his own body but yielding it to his wife?

I'm interested in an overview of the views of various Christian denominations on this, or other forms of consensual (on the part of both/all parties) open marriages - are there any that consider them to be okay?
I am unable to find reference to any official sects or doctrines which permit open-relationships (as distinct from polygamy and various forms of plural marriage).  However, there certainly are a minority of Christians who practice various forms of open-relationships. The Liberated Christians web site* has a section about various forms of open relationships within a Christian context.  As far as I know, it's a completely amateur site, run by volunteers, and without the backing of any official church organization, denomination, or sect.
An overview of their beliefs is explained here, and says, in part:

The ancient Hebrews, as portrayed in the Old Testament, clearly believed in multiple partnerships and this practice is nowhere condemned by God.
When the New Testament scriptures are viewed as a whole, taking into account the cultural context in which they were written, it is clear that neither Jesus nor the writers of the New Testament condemned such practice, although it appears that polygamy had, for non-religious reasons, substantially declined within Jewish culture by the time of Christ.
Despite this biblical evidence, the Christian church has persistently opposed polygamous relationships and has, at times, actively persecuted families which chose to practice this lifestyle. The church has also used twisted interpretations of various scriptures in defense of its opposition to this lifestyle.

And they describe those who agree with them as:

Many of them are mainstream, evangelical Christians, including pastors and their wives, church elders and Sunday school teachers. Some are seminary-trained theologians. Others are lay men and women from many different church backgrounds or no organized Christian background at all. They come from all walks of life, including college students, doctors, ministry professionals, housewives and blue-collar workers. They may be your neighbors, co-workers or even your relatives. (Scary, isn't it?!) They are ordinary people who have simply acknowledged that they have polyamorous desires, as do most other people who are unable to admit it to themselves, their partners, their church or their God.

So not really a sect, per-se, but there are a number of Christians purported to share their views.
*Warning: ancient web site, with poor taste in animated gifs, and many broken links!