poincare symmetry - Is there a type of supersymmetry where supercharges have spin 3/2?

Thinking of supersymmetry operators $Q$, they mix fields with a certain spin with fields with spin $1/2$ higher or lower.

Thinking of open bosonic strings from string theory, the different modes are separated by integer spin.

Thinking of bosonic closed string theory, the different modes are separated by twice integer spin.

So these are three types of theory with particles of only spins $N/2, N$ and $2N$.

(In the supersymmetry case there are only finite number of fields from spin -2 to 2 but lets ignore this small fact!)

So to complete the set it seems reasonable to think there might be a theory in which only has fields of spin $3N/2$. As an example it might contain just spin $\pm 3/2$ gravitinos and spin $0$ scalars. Is any such symmetry known to exist? i.e. it would be a symmetry that mixed gravitinos with scalars without any other fields.

I don't know what the algebra would be but it should presumably have a spin 3/2 operator $R$ and some rule like:

$$\{R^\alpha_\mu, R^\beta_\nu\} = f^{\alpha\beta}_{\mu\nu\tau\sigma\omega}P^\tau P^\sigma P^\omega.$$