Is there a field equation which can reduce into all three flavors of spin (zero, one, one half)?

Is there a known particle field equation of a similar form

$$\begin{equation} (\Gamma^n \pi_n)^2 \Psi = (mc)^2 \Psi \tag{1} \end{equation}$$ such that by reducing the number of degrees of freedom for the spinor $\Psi$ into a spinor of lesser degrees of freedom, such as a scalar $\psi_0$, two three-vectors $\boldsymbol{\psi}_\pm$ or two two-vectors $\boldsymbol{\phi}_\pm$, it reduces Eq. 1 into either ...

• a spin zero field equation $$\begin{equation} \pi^n \pi_n \psi_0 = (mc)^2 \psi_0, \tag{2} \end{equation}$$


• a spin one field equation $$\begin{equation} (I\pi_0\pm i \boldsymbol{\pi} \times) (I\pi_0\mp i \boldsymbol{\pi} \times) \boldsymbol{\psi}_ \pm = (mc)^2 \boldsymbol{\psi}_ \pm \tag{3} \end{equation}$$


• or a spin 1/2 field equation $$\begin{equation} (I\pi_0\pm\boldsymbol{\sigma}\cdot\boldsymbol{\pi}) (I\pi_0\mp\boldsymbol{\sigma}\cdot\boldsymbol{\pi}) \boldsymbol{\phi}_\pm = (mc)^2 \boldsymbol{\phi}_\pm? \tag{4} \end{equation}$$

In these expressions $\pi_n$ is the four-component momentum operator which includes the electromagnetic four-potential interaction $A_n$ with the particle's charge $q$ written as

$$\begin{equation} \pi_n = i\hbar \partial_n - q A_n , \tag{5} \end{equation}$$ and $$\begin{equation} \boldsymbol{\pi} = -i\hbar \boldsymbol{\nabla} - q \boldsymbol{A} \tag{6} \end{equation}$$ uses bold to indicate a euclidean vector, specific to 3-components. The three two-by-two matrices $\boldsymbol{\sigma}$ in Eq. 4 are the Pauli Spin Matrices.