Some like to point out that elders are always spoken of in Scripture in the plural, thus purportedly showing that it is unscriptural to have a single elder/pastor/overseer leading a flock. This is, however, not conclusive proof in my opinion. The Bible does indeed mention that, in certain cities, more than one elder was overseeing the church, but it does not say that those elders were co-equal over one individual congregations. For example, when Paul gathered the elders from Ephesus (see Acts 20:17), it is quite obvious that those elders were from a city in which the overall body consisted of thousands and perhaps tens of thousands of people (see Acts 19:19). Thus there had to have been many flocks in Ephesus, and it is quite possible that each individual elder oversaw an individual house church.
There is no example in Scripture where God called a committee to do any task. When He wanted to deliver Israel from Egypt, He called one man, Moses, to be the leader. Others were called to help Moses, but all were subordinate to him, and like him, they each had individual responsibility over a certain sub-group of people. This pattern is repeatedly found in Scripture. When God has a task, He calls one person to take responsibility, and He calls other to help that person.
Thus it seems unlikely that God would call a committee of elders of equal authority to oversee every little house church of twenty people. It seems like an invitation for strife.
This is not to say that every house church should be overseen by one and only one elder. It is to say, however, that if there is more than one elder in a church, the younger and less spiritually mature elder(s) should submit to the oldest and most spiritually mature elder. Scripturally, it is the churches, not Bible Schools, that are supposed to be the training grounds for young pastors/elders/overseers, and so it is quite possible and even desirable for there to be several elders/pastors/overseers in a house church, with the spiritually younger being discipled by the spiritually older.
I have observed this phenomenon even in churches that are supposedly overseen by “equal” elders. There is always one who is looked up to by the others. Or there is one who is dominant while the others are more passive. Otherwise there is strife eventually. It is a fact that even committees always elect one chairperson. When a group of equals sets out to do a task, they recognize that there must be one leader. So it is in the church.
Additionally, the responsibility of elders is compared to the responsibility of fathers by Paul in 1 Timothy 3:4-5. Elders must manage their own households, otherwise they are not qualified to manage the church. But how well would a family with two equal fathers be managed? I suspect there would be problems.
Elders/pastors/overseers should be networked in the larger local body so there is mutual accountability among fellow-elders who can help if there is ever a problem that requires them. Paul wrote of a “presbytery” (see 1 Tim. 4:14), which must have been a meeting of presbuteros (elders) and possibly other men with ministry gifts. If there is a founding apostle, he too can be of service if there are problems in a local body that are the result of an elder who has erred. When institutional pastors go astray, it always results in big problems because of the structure of the church. There is a building and programs to maintain. But house churches can be instantly dissolved when a pastor goes astray. The members can simply join another body.