Most theories of punishment are monist. One is usually either a retributivist, a deterrence theorist, or a rehabilitationist. That is, most people think one of these kinds of theory about punishment is sufficient to justify punishment.
It also seems that most people do not think that they can work together. So a theory which combines retributivism and deterrence is taken to be impossible or nonsensical, or perhaps merely unnecessary.
I think, contrarily, that punishment can be pluralist: It can incoroporate multiple of these perspectives.
Pluralism can, I take it, come in a weak and a strong form. The weak form of pluralism merely states that no monist theory of punishment is sufficient across the range of situations in which it is to be applied. Applying only retributivism will not provide justified/defensible outcomes in all the situations in which applying punishment is appropriate. This seems the case. But I would go further, and argue for a strong form of pluralism. According to a strong form of pluralism about punishment, not only is no single perspective sufficient across the whole range of cases, but there is also no consistent ordering of the theories of punishment, capable of general application. That is, it is not the case that Retributivism ought always to be the primary consideration, with rehabilitation and deterrence modifying the retributively established outcome. Rather, sometimes deterrence is primary, sometimes rehabilitation is primary.
This approach is more difficult to defend. It requires a mechanism for determining the circumstances in which each of the plural approaches is primary, and probably also a weighting mechanism for combining their commands into a coherent description of the appropriate course of action when confronted with any particular circumstance requiring punishment. But I think it is a better place to begin than are the monist positions.