We consider the possibility of several different mechanisms contributing to the $(\beta \beta {)}_{0\nu }$-decay amplitude in the general case of $CP$ nonconservation: light Majorana neutrino exchange, heavy left-handed and heavy right-handed Majorana neutrino exchanges, lepton charge nonconserving couplings in supersymmetry theories with $R$-parity breaking. If the $(\beta \beta {)}_{0\nu }$ decay is induced by, e.g., two “noninterfering” mechanisms (light Majorana neutrino and heavy right-handed Majorana neutrino exchanges), one can determine $|{\eta }_i{|}^2$ and $|{\eta }_j{|}^2$, ${\eta }_i$ and ${\eta }_j$ being the two fundamental parameters characterizing these mechanisms, from data on the half-lives of two nuclear isotopes. In the case when two “interfering” mechanisms are responsible for the $(\beta \beta {)}_{0\nu }$ decay, $|{\eta }_i{|}^2$ and $|{\eta }_j{|}^2$ and the interference term can be uniquely determined, in principle, from data on the half-lives of three nuclei. Given the half-life of one isotope, the “positivity conditions” $|{\eta }_i{|}^2\ge 0$ and $|{\eta }_j{|}^2\ge 0$ lead to stringent constraints on the half-lives of the other $(\beta \beta {)}_{0\nu }$-decaying isotopes. These conditions, as well as the conditions for constructive (destructive) interference are derived and their implications are analyzed in two specific cases. The experimental limits on neutrino masses obtained in the ${}^{3}H$ $\beta$-decay experiments can constrain further the multiple mechanisms of $(\beta \beta {)}_{0\nu }$ decay if one of the mechanisms involved is the light Majorana neutrino exchange. The measurements of the half-lives with rather high precision and the knowledge of the relevant nuclear matrix elements with relatively small uncertainties is crucial for establishing that more than one mechanism are operative in $(\beta \beta {)}_{0\nu }$ decay. The method considered by us can be generalized to the case of more than two $(\beta \beta {)}_{0\nu }$-decay mechanisms. It allows us to treat the cases of $CP$ conserving and $CP$ nonconserving couplings generating the $(\beta \beta {)}_{0\nu }$ decay in a unique way.

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