Total Spin of Two Particles w/ Spin 1

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I have a noobish question on spin addition. If I have a system of two particles, each with spin 1, and the spins don't interact, what is the total spin of the system (assuming zero orbital angular momentum)? Is the total spin just 2?

(I hope that my reach hasn't exceeded my grasp here.)
 
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The total spin (I assume you mean the quantum number that corresponds to the magnitude of the spin angular momentum, without regard to the direction) can be either 0 or 1 or 2.
 
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Thanks jtbell, I should have specified that the particles are massless so that each has only two possible spin states (+ or - 1). On this basis, I would imagine that the system can only have two possible spin magnitudes, 0 or 2 (and not 1). Is this correct?
 

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