There are other non-denominational groups which are called by outsiders “Plymouth Brethren” (because the first ones met together in Plymouth, England). They were started by William Craig and George Müller who found that they were not permitted to have communion in traditional churches unless they joined that particular sect. That they wouldn’t do since they recognized the Christian Church as a single entity founded by our Lord Himself. They rejected sectarianism as a man-made institution. So they met together with other believers “in the name of Christ alone.” These brethren continue to this day. They have communion every Sunday, and body ministry (each male member of the local assemblies can minister to the whole group as he is led of the Spirit. Sisters must keep silent in accordance with the words of Paul in I Timothy 2:12. During the meeting sisters may open their mouths only to join in singing hymns). Any brother (not necessarily an elder) may give thanks for the bread or the wine. These brethren have elders and deacons that are recognized by their ministry rather than being appointed. “Plymouth Brethren” do not practice open communion.
There are 9 different circles of fellowship among them. The beliefs of all 9 are identical. They differ only in the way they accept people for communion. The communion is central to their Sunday morning meeting. All hymns and prayers in that meeting center around the Lord Jesus and what He did for them by his death on the cross. I’ll mention just 3 of their circles and their positions on communion.
The "open brethren"
It was with one of the assemblies of this circle that I used to fellowship. The only reason I don’t do so now, is that I have moved back to the area where I was born, where there are no brethren assemblies. If a visitor or a stranger enters the Sunday morning meeting, he is greeted by the deacons at the door. By questioning the visitor, they try to determine whether he is a Christian, and if they are convinced that he is, they invite him to participate fully. He can not only take communion, but he can minister by suggesting a hymn, praying aloud, giving a short talk, etc. If they sense that he is not a Christian, he is invited to sit on a pew at the back as an observer. The bread and wine are not passed to that bench, and neither is the collection bag (the brethren consider it wrong to accept money from non-Christians).
**The “tight brethren” **
Similar to the open brethren in many ways, except on the communion issue. In order to participate in communion at an assembly of this circle, one must apply to the elders some time prior to attending. I once attended one of these assemblies, but was not permitted to take communion since I had not applied to the elders in advance.
The "exclusive brethren"
These brethren were headed by J.N. Darby. I think it is impossible for an outsider to take communion with these folks.