God has ONE people, the Church (Israel), and no others. The broken off unbelieves can only become Israel upon accepting Christ.
“Having abolished in his flesh the enmity, even the law of commandments contained in ordinances; for to make in himself of twain one new man, so making peace; And that he might reconcile both unto God in one body by the cross, having slain the enmity thereby: And came and preached peace to you which were afar off, and to them that were nigh. For through him we both have access by one Spirit unto the Father. Now therefore ye are no more strangers and foreigners, but fellowcitizens with the saints, and of the household of God;” Ephesians 2:15–19 (KJV 1900)