Pricing a European call option while absence of arbitrage is violated
I believe there is not a unique price. Say, instead of buying the option  you spent 0.5 on a half a unit of the asset $S^2_1$ This asset pays out $[0.4, 0.6, 0.8]$ which first order stochastically dominates the option. So, no matter your probability beliefs about the states,  in that setting you'd never pay $0.5$ for the option which pays less in every state. This suggests the right price is less than $0.5$. Similarly, buying $0.25$ units of the $S^0_1$ asset or $0.167$ units of the $S^1_1$ asset would likewise stochastically dominate the option. In fact, because for $0.375$ units of asset $S^1_2$, which costs on $0.375$, you can still have an asset that pays out $[0.3, 0.45, 0.6]$, it seems unlikely that the price could even be as high as $0.375$. Asset 0 implies a price below $0.4$ and asset 1 below $0.45$

Some python code to solve:

import numpy as np
S0 = np.array([[2],[3],[1]])
D = np.array([[1,2,3], [2,2,4], [0.8, 1.2, 1.6]])
X = np.array([[0.0],[0.2],[0.6]])
phi = np.dot(np.linalg.inv(D.transpose()), X)
print('The weights of the portfolio that replicates payoff X are: \n', phi)
P_X = np.dot(S0.transpose(), phi)
print('With a price: ', P_X)
print('Normalizing to pay a fixed price P_X for each of the three assets, what payoffs can you get?')
D_norm = D/(2*S0)
print(D_norm)
print('Notice that all three first order stochastically dominate the option for a price of: ', P_X)
print(D_norm - X.transpose())
print('Using each of the base assets, what\'s the minimum quantity that dominates?')
D_relative = X.transpose() / D
print(D_relative)
Min_dominating_fraction = np.max(D_relative,axis=1)
print('Minimum fraction of each of the assets that dominates X\n', Min_dominating_fraction)
P_Min_dominating_fraction = S0.transpose() * Min_dominating_fraction 
print('At prices of: ', P_Min_dominating_fraction)
print('Therefore the option price should be less than: ', np.min(P_Min_dominating_fraction))


This code doesn't spell out the price of the option, it just show my calculations for the paragraph above. I believe the real price of this option would actually be zero if shorting is permitted. If you buy three units of asset $S^2_0$  and short one unit of $S^1_0$ you get an asset with payouts $[ 0.4,  1.6,  0.8]$. This position costs nothing to take, has positive payouts for all states, and first order stochastically dominates the option itself. Since it is possible to make a better than replicating portfolio at zero cost the price should be zero. Oh the insanity at work when arbitrages are present!