Can anyone write another book to go in the Bible?
This is a complicated question, so bear with me.
The Bible, as it stands today, is a historical document that covers the Jewish people and their early ancestors (before the time they formed their first collective nation) through the times of the early church and the extension of God's grace to the Gentiles. It has minor references to the times and state of the earth before Adam and Eve, and devotes many chapters and portions of chapters in both the Old and New Testaments to the very end times of the earth from the time of Christ's return for His church onward, with descriptions of heaven and the final way things will end up.
Keep in mind that as far as the New Testament is concerned, many books between the Gospels and Revelation are simply letters written from a few apostles to churches. Many such letters could be written today to address church problems and would be just as relevant to all Christian's lives as those early letters were. However, while it is possible that someone could write another book that would be worthy of being added to the New Testament - a "Letter to the church of San Francisco" or "Letter to the church of New York City" or "Letter to the church of Paris" or "Letter to the Chinese", for example - tradition and the lack of stature of the author would probably preclude anyone actually adding it to make a new canon of scripture.
It should be noted that there are various versions of the Bible in print today with different canons. The Catholic church, and some close denominational relatives, accept a few more books in their versions of the Bible than the Protestant churches by and large accept. In some cases, the Protestants chose to not include certain books because they felt that portions of those books were not in harmony with the rest of the Bible or actually were contradictory. In some cases the books themselves disclaim being divinely inspired. In other cases, the books - particularly minor Jewish history books - were deemed to be in harmony, but did not add anything significant to the other books. Printing costs - and hand copying costs in the early days - led to a core set of books for each group that has remained unchanged for a very long time.
If new caches of early manuscripts were uncovered in multiple locations, and these early manuscripts included a previously unknown book that had multiple sources and was deemed worthy of being included in the Bible by Catholics and Protestants alike, both for unique information and lack of conflict with established canon, it would be interesting to see the result. It is likely that the Bibles would still stay as they are and the new work would be made available as a companion book since tradition in all aspects of Christianity is strong.
The lack of conflict with the established text cannot be stressed enough.
The Church of Jesus Christ of the Latter Day Saints was formed by Mr. Joseph Smith, Jr. claiming to have received a new revelation on golden tablets he was directed to by an angel (Gal. 1:6-12). However, this new revelation is in conflict with the existing text of the Bible in many respects, presenting new doctrines and means of salvation which are not in harmony with the received text at all - from salvation by proxy baptism which is why they care so much about genealogy, to who Christ was, to what man was, to what righteous men become after death, to the nature of God himself (Lk. 20:28-35; 1 Tim. 1:3-4; Titus 3:4-11).
Therefore, both Catholic and Protestant churches reject his book as uninspired and false. It will never become part of the Christian Bible. The LDS denomination is rejected as being Christian, regardless of the use of Jesus Christ in its name. One should always keep the warnings of scripture in mind when looking at any religious work (including this website as my sites have been attacked and defaced at times) or organization and rely primarily on the Bible as your source of study.
On the other hand, God, through the Holy Spirit, provided gifts to His new church including the gift of prophecy and of tongues and interpretation of tongues, words of knowledge, and words of wisdom (1 Cor. 12-14). Pentecostal denominations in the Christian church believe these provide timely messages to bodies of people through the Spirit filled believer that are directly from God. If these were collected together, they could form a new book. However in most cases, there is no effort made, even with today's technology, to collect and publish these words. I've tried on my awmach.org website to collect a few of these.
In all cases, any new word received in this way must meet the same standards as applied to an existing book. It should be in harmony with the Bible and with what we know of the nature of God from it. It should uplift or correct and not lead people to sin or attempt to introduce some new doctrine or theory that is different than what the Bible says (2 Tim. 3:1-4:5). The gift of discerning of spirits which is another gift of the Spirit that God gave to Spirit filled believers, is useful in this regard to sort out anything that is not from God.