What verses are commonly cited to support that unity, despite differences, is preferable to dividing the Church? If you're involved in church leadership/management, then you are keenly aware of the real threat that differences in doctrine can pose to the unity of the church. If you know anything about the Reformation, then you know that differences in doctrine are pretty much the only reason churches have split in the past.

However, some denominations strongly stress unity over doctrine. Catholicism seems to be one. Anglican, Episcopal, and some Presbyterians seem to stress unity as well. Or, in other words, they allow members and even leadership to espouse dissenting doctrinal opinions, at least on minor issues, preferring to focus on what they do share, which is brotherhood in Christ.

My first thought is that a house divided against itself cannot stand. Powerful words, however, they seem to stress unity in purpose rather than doctrine. With a bit of thought, it's obvious that the Church body must at least be unified in purpose (presumably to glorify God in everything and show the world his light), but some argue there is plenty of room for differing opinions on some or even most doctrinal issues. What is the biblical basis for this opinion?
Verses regarding unity of doctrine are not as common as the less specific verses regarding unity as a body.  Two verses that I have most commonly heard referenced regarding avoiding doctrinal division are:


  But avoid foolish controversies, genealogies, dissensions, and quarrels about the law, for they are unprofitable and worthless. - Titus 3:9 ESV


And


  Have nothing to do with foolish, ignorant controversies; you know that they breed quarrels. - 2 Timothy 2:23 ESV


But it could be argued that both reference all controversy, and are not limited to church leadership.  

One the other hand, Paul addresses this very issue of church doctrinal unity in his first letter to the church in Corinth, and I rarely if ever hear this referenced in that context:


  10 I appeal to you, brothers, by the name of our Lord Jesus Christ, that all of you agree, and that there be no divisions among you, but that you be united in the same mind and the same judgment.
  11 For it has been reported to me by Chloe's people that there is quarreling among you, my brothers.
  12 What I mean is that each one of you says, "I follow Paul," or "I follow Apollos," or "I follow Cephas," or "I follow Christ."
  13 Is Christ divided? Was Paul crucified for you? Or were you baptized in the name of Paul?
  14 I thank God that I baptized none of you except Crispus and Gaius,
  15 so that no one may say that you were baptized in my name.
  16 (I did baptize also the household of Stephanas. Beyond that, I do not know whether I baptized anyone else.)
  17 For Christ did not send me to baptize but to preach the gospel, and not with words of eloquent wisdom, lest the cross of Christ be emptied of its power. - 1 Corinthians 1:10-17 ESV 


A few others that may also be useful in this regard:


  17 I appeal to you, brothers, to watch out for those who cause divisions and create obstacles contrary to the doctrine that you have been taught; avoid them.
  18 For such persons do not serve our Lord Christ, but their own appetites, and by smooth talk and flattery they deceive the hearts of the naive. - Romans 16:17-18 ESV


And


  24 But God has so composed the body, giving greater honor to the part that lacked it,
  25 that there may be no division in the body, but that the members may have the same care for one another.
  26 If one member suffers, all suffer together; if one member is honored, all rejoice together. - 1 Corinthians 12:24-26 ESV


And


  17 But you must remember, beloved, the predictions of the apostles of our Lord Jesus Christ.
  18 They said to you, "In the last time there will be scoffers, following their own ungodly passions."
  19 It is these who cause divisions, worldly people, devoid of the Spirit. - Jude 1:17-19




I have edited again to include a verse that I almost literally stumbled upon recently (printed on a floor plaque outside a church):


  1 So if there is any encouragement in Christ, any comfort from love, any participation in the Spirit, any affection and sympathy,
  2 complete my joy by being of the same mind, having the same love, being in full accord and of one mind. - Philippians 2:1-2 ESV