The term "fitted together" certainly gives us a picture of a very tight relationship. Stones fitted together by a skillful builder are chosen and placed in such a way that they form a single wall that is beautiful to behold. No stone stands out and no stone is unimportant. Note that the stones are not free to choose their own place in the wall, but that their position is selected according to the wisdom and skill of the craftsman.
Is this not also God's way? In Paul's teaching on the functioning of the body of Christ in 1 Corinthians 12:12-31, he makes it clear that God sets each one in the body according to His divine wisdom. When each member accepts his own position under the authority of Christ and moves in the grace that God has given, the whole body moves as one to do the will of God and express the life of God. No member is complete apart from the other members, and each has an important function according to God's design.
For this to function in reality, there must be a proper relationship between all the members. Each must know his own place, not thinking he is more important than the others, nor thinking that he is unimportant. The whole body is to function in the order of God as the Spirit directs. I think we know from experience that such a close functioning is not a simple matter. For this to happen, the body must be "fitted together" by God.
To be fitted together in the manner described by Paul takes the divine work of God, but it also means that each member is alive to God and responding to God. This cannot be just a theory or a wonderful ideal. Each member must be holding fast to the Head in a living relationship with God. In the words of Jesus in John 15, each one must be abiding (living) in the vine. If this is not true, it will be absolutely impossible to work out the functioning that Paul speaks about.
A result of being in submission to Christ's authority will be a submission one to another. "Likewise you younger people, submit yourselves to your elders. Yes, all of you be submissive to one another, and be clothed with humility, for 'God resists the proud, but gives grace to the humble'" (1 Peter 5:5). This is in keeping with the truth John speaks (in 1 John): that it is impossible for someone to love God and not love his brother. Paul tells us that this is a fruit of "being filled" with the Spirit of God (Ephesians 5:17-21).
An attitude of submission toward every other member of the household puts me in a right relationship to be able to serve and receive. Both are always "unto the Lord" for He is the Head. There is no "hierarchy" in the household, but there are different measures of grace. The grace and callings are according to the wisdom of God, and as we maintain this humble and submissive attitude toward every member, we open ourselves up to the supply of God's grace under the direction of the Holy Spirit.
Perhaps another way we can look at this "fitting together" is to remember that love "adjusts" to fit in with others. This does not mean we compromise truth or overlook sin. We are speaking about being sensitive to other members and adjusting our communication and relationship to "fit together" in harmony as we do the will of God together. The closest natural example is the marriage relationship, but fitting together in the Spirit is even more demanding because we are dealing with spiritual matters and there are many more people involved.
To be able to fit together, we must allow God to change us. Yet is this not what He is doing? "But we all, with unveiled face, beholding as in a mirror the glory of the Lord, are being transformed into the same image from glory to glory, just as by the Spirit of the Lord" (2 Corinthians 3:18). The key is "beholding as in a mirror the glory of the Lord." We do not behold each other. We must behold the Lord. As we behold the Lord, He will change us "from glory to glory." Change is usually not easy, but when we experience the grace of the Lord and begin to see as He sees, it is a glorious working, filled with the presence of God. Each change is glorious, but there is always more. As God changes us into His likeness, we will be able to fit together in greater and greater harmony. The changes are real. God is changing how we think, how we speak, and what we do. We really are being changed into His glorious likeness, to be a true expression of His life together.