Scriptures below are quoted from the King James Bible, which is based on the Textus Receptus.
The main arguments I am aware of can be grouped into the following categories.
It is a principle first found in the law that you need at least two witnesses to establish the truth. (Deuteronomy 17:6; 19:15)
2 Corinthians 13:1 This is the third time I am coming to you. In the mouth of two or three witnesses shall every word be established.
Proverbs 11:14 Where no counsel is, the people fall: but in the multitude of counsellors there is safety.
The majority text follows the multitude of witnesses. With the Alexandrian type texts, there are many differences even in the two main witnesses the Sinaiticus and Vaticanus.
Preservation of Scripture
There are many scriptures talking about the preservation of God's word. Under the Textus Receptus tradition the text is assumed to be preserved. The critical manuscripts based on the Alexandrian texts assumes the originals are lost, in contradiction with scripture.
Psalms 100:5 For the Lord is good; his mercy is everlasting; and his truth endureth to all generations.
Psalms 119:152 Concerning thy testimonies, I have known of old that thou hast founded them for ever.
Isaiah 40:8 The grass withereth, the flower fadeth: but the word of our God shall stand for ever.
John 10:35 If he called them gods, unto whom the word of God came, and the scripture cannot be broken;
A point is made here that Timothy had the scriptures:
2 Timothy 3:15 And that from a child thou hast known the holy scriptures, which are able to make thee wise unto salvation through faith which is in Christ Jesus.
So Timothy is either using the original autographs as a child or, more likely, the copies he had were scripture and therefore preserved.
There are many more texts around preservation.
Spiritual condition of Egypt and Alexandria compared to Antioch
Egypt was a land of idolatry and false worship. God plagued Egypt and saved Israel out of Egypt (Exodus 9-12). Egypt is used in Revelation to characterize spiritual wickedness.
Revelation 11:8 And their dead bodies shall lie in the street of the great city, which spiritually is called Sodom and Egypt, where also our Lord was crucified.
The Alexandrian type texts originate from Alexandria which is in Egypt and would be an odd place for God then to use as the best source for his word.
Alexandria comes up in the new testament as a place where people came and set up false witnesses against Stephen (Acts 6:9-14).
In contrast Antioch was a stronghold of Christianity:
Acts 11:26 And when he had found him, he brought him unto Antioch. And it came to pass, that a whole year they assembled themselves with the church, and taught much people. And the disciples were called Christians first in Antioch.
Acts 15:35 Paul also and Barnabas continued in Antioch, teaching and preaching the word of the Lord, with many others also.
The Byzantine type texts are sometimes called Antiochian.
Recorded attacks on the word of God
It is argued against the Textus Receptus, that the Alexandrian type texts are only fourth century and therefore earlier. However scripture records there were attacks on the word of God before this time, so the Alexandrian manuscripts could be examples of this.
2 Corinthians 2:17 For we are not as many, which corrupt the word of God: but as of sincerity, but as of God, in the sight of God speak we in Christ.
Acts 20:29-30 For I know this, that after my departing shall grievous wolves enter in among you, not sparing the flock.
30 Also of your own selves shall men arise, speaking perverse things, to draw away disciples after them.
Greater consistency of the text
Following on from the idea of preservation is the observation that the Textus Receptus is more consistent, which we hope it is because the Word of God is true.
Psalms 119:160 Thy word is true from the beginning: and every one of thy righteous judgments endureth for ever.
For example, in the critical texts Mark 1:2 attributes two scriptures to Isaiah which are actually quoted from Malachi and Isaiah. In contrast the TR is consistent by just saying "prophets":
Mark 1:2 As it is written in the prophets, Behold, I send my messenger before thy face, which shall prepare thy way before thee.
When the TR is attacked the attacks fail. For example, there appears to be a similar problem in all texts:
Matthew 27:9 Then was fulfilled that which was spoken by Jeremy the prophet, saying, And they took the thirty pieces of silver, the price of him that was valued, whom they of the children of Israel did value;
The apparent problem is the text attributed to Jeremiah belongs to the book Zecharaiah. However, a proper study of Ezra, Nehemiah and Zecharaiah reveals that there is a Jeremiah around about the time of Zechariah, and the quote is from portions of Zechariah not attributed to prophet Zecharaiah explicitly.
There are of course many thousands of textual differences to consider.
Finally it can be argued that the Textus Receptus has better doctrine. What is better doctrine comes down to hearing.
John 10:27 My sheep hear my voice, and I know them, and they follow me:
It is then up to individuals to looks at texts with questionable doctrine and decide which one is more accurate. Taking care not to be deceived
For example the Textus Receptus is very careful to not call Joseph Jesus' father, which the critical texts freely do. (e.g. Luke 2:33)
John 3:16 For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.
Some translations leave out the word begotten allowing for the doctrine that Jesus was born of Joseph but became a son of God.
There are dozens of important examples to consider.