α-like four-nucleon correlations are included in the structure of superfluid ground and low-lying excited states of atomic nuclei within a BCS-like approach. New metastable superfluid and normal states are predicted. These states could be associated with some of the recently discovered Iπ = 0+ states in different regions of atomic nuclei. A new type of elementary excitations may be constructed on these metastable states in the same way as those constructed on the BCS superfluid ground states. The region of superfluid cold nuclei is enlarged due to the fact that the neutron and proton superfluidity can mutually be induced via the α-like four-nucleon ineractions. This type of correlations lead to a further enhancement of the probabilities of the favoured α-clusterization processes (such as α-decay or α-transfer reactions), two-nucleon transfer reactions and other clusterization processes such as e.g. the heavy cluster decay.