How do I add the spin angular momentum of massless particles, like photons, where only the transverse polarizations are allowed?

If all three polarizations were allowed, this would be an easy exercise: you'd get $S=0,1,2$ states. But some of these states clearly aren't allowed for purely transverse photons: For example, with a photon moving in the same direction as quantization axis, the state

$$\big|S=2,M=1\big\rangle=\frac{1}{\sqrt{2}}\big(|m_1=1,m_2=0\rangle+|m_1=0,m_2=1\rangle)$$

contains the $m=0$ state which is not allowed.

Edit: In the spectroscopic notation, which states are allowed?

How do I add the spin angular momentum of massless particles, like photons, where only the transverse polarizations are allowed?

If all three polarizations were allowed, this would be an easy exercise: you'd get $S=0,1,2$ states. But some of these states clearly aren't allowed for purely transverse photons: For example, with two photons moving in the same direction as quantization axis, the state

$$\big|S=2,M=1\big\rangle=\frac{1}{\sqrt{2}}\big(|m_1=1,m_2=0\rangle+|m_1=0,m_2=1\rangle)$$

contains the $m=0$ state which is not allowed.

Edit: In the spectroscopic notation, which states are allowed?