A premix burner arrangement for safely oxygen-enriching a premix air-fuel combustion system is disclosed. In the disclosed burner arrangement, a first conduit is arranged and disposed to provide a first gas stream. The first gas stream is a self-reactive or self-flammable premixture comprising air and a combustible gas. At least one second conduit is arranged and disposed to provide a second gas stream circumferentially around the first gas stream. The second gas stream includes oxygen. The premix burner arrangement is configured to combust or react the first stream at a temperature at least 1000° F. greater than the temperature of the second stream. A method and combustion system including the premix burner arrangement are also disclosed.