For the B2 Coxeter arrangement with multiplicities (2,k,1,k), k>=4, no free extension exists, and this obstruction transfers to Bn and to explicit B3 multiplicities.
Abe, Chambers of 2-affine arrangements and freeness of 3-arrangements , J
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Extendability of the $B_2$-arrangement
For the B2 Coxeter arrangement with multiplicities (2,k,1,k), k>=4, no free extension exists, and this obstruction transfers to Bn and to explicit B3 multiplicities.