What is the Scriptural basis for Modalism? We hear a lot at times about the godhead, so that got me wondering: what is the Scriptural basis for the Christian doctrine of Modalism?
The United Pentecostal Church International, who are a denomination of Oneness Pentecostalism, and adopt the doctrine of Oneness, which is essentially the same as Modalistic Monarchianism, offer the following in support of their Doctrinal Foundation:


  The Oneness of God
  
  God is absolutely and indivisibly one (Deuteronomy 6:4;
  Galatians 3:20). In Jesus dwells all the fullness of the Godhead
  bodily (Colossians 2:9). He is the self-revelation of the one
  God, the incarnation of the full, undivided Godhead (John 20:28;
  I Timothy 3:16).
  
  God has revealed Himself as Father (in parental relationship to
  humanity), in the Son (in human flesh), and as the Holy Spirit (in
  spiritual action).  (See Deuteronomy 32:6 and Isaiah 63:16;
  Luke 1:35 and Galatians 4:4; Genesis 1:2 and Acts
  1:8.) The one God existed as Father, Word, and Spirit before His
  incarnation as Jesus Christ, the Son of God; and while Jesus walked on
  earth as God Himself incarnate, the Spirit of God continued to be
  omnipresent. However, the Bible does not teach that there are three
  distinct centers of consciousness in the Godhead or that Jesus is one
  of three divine persons.
  
  Jesus is true God and true man as one divine-human person. We can
  distinguish these two aspects of Christ’s identity, but we cannot
  separate them. The Incarnation joined the fullness of deity to
  complete humanity.
  
  Jesus possessed all elements of authentic humanity as originally
  created by God, without sin. Thus we can speak of Jesus as human in
  body, soul, spirit, mind, and will. (See Matthew 26:38; Luke
  2:40; 22:42; 23:46; Philippians 2:5.) According
  to the flesh, Jesus was the biological descendant of Adam and Eve,
  Abraham, David, and Mary. (See Genesis 3:15; Romans 1:3;
  Galatians 3:16; Hebrews 2:14-17; 5:7-8.) We should
  not speak of two spirits in Jesus, however, but of one Spirit in which
  deity and humanity are joined.
  
  Christ’s humanity means that everything we humans can say of
  ourselves, we can say of Jesus in His earthly life, except for sin. In
  every way that we relate to God, Jesus related to God, except that He
  did not need to repent or be born again. Thus, when Jesus prayed,
  submitted His will to the Father, and spoke about God, He simply acted
  in accordance with His genuine humanity.
  
  As Jehovah manifested in the flesh, Jesus is the only Savior (Isaiah
  45:21-23; Matthew 1:21-23). Thus, Jesus is the only name
  given for our salvation (Acts 4:12). The Father was revealed to
  the world in the name of Jesus, the Son was given the name of Jesus at
  birth, and the Holy Spirit comes to believers in the name of Jesus.
  (See Matthew 1:21; John 5:43; 14:26; 17:6.)
  Thus, the apostles correctly fulfilled Christ’s command in Matthew
  28:19 to baptize “in the name [singular] of the Father, and of the
  Son, and of the Holy Ghost” by baptizing all converts with the
  invocation of the name of Jesus.


Source: Our Doctrinal Foundation; United Pentecostal Church International