Such action as is mentioned in this question is usually described as a sponsoring church arrangement. This is where one local church “sponsors” a work bigger than what they are able to handle as a local church. Therefore, they solicit funds from other local churches so that they will be able to do a work that they could not do alone, such as preaching the gospel on television. The bottom line is, there is absolutely no principle in scripture, either by command, example, or necessary inference, that would authorize churches pooling their funds for the purpose of an evangelistic work. When Paul was in need of monetary support while he was at Corinth, churches in Macedonia sent to provide for him (II Corinthians 11:7-9). In Philippians 4:15-16, Paul says that the church at Philippi was the first to send to him to provide for his needs. In each case, money was sent directly from each church to the preacher that was being supported. This money was not sent to Corinth, who in turn provided support for Paul. Nor did the church at Philippi become a sponsoring church collecting funds from other churches for Paul’s needs.
We must remember that elders only have oversight of the flock “among them” (I Peter 5:1-2). They have no right to take oversight of the affairs of another church.