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This paper investigates the cosmological dynamics arising from the interaction between a 2-form field and cold dark matter within a Bianchi I background. Employing a dynamical system analysis, we identify two attractors yielding to exponential expansion of the Universe, i.e., de-Sitter solutions. Notably, these solutions exhibit a pivotal distinction: one is indistinguishable from the cosmological constant scenario, while the other corresponds to an \emph{anisotropic de-Sitter} expansion sourced by the 2-form field. To validate the asymptotic behavior of our model, we conduct a numerical exploration of its expansion history. Our analysis reveals that the coupling between the dark sectors amplifies the shear during the matter-dominated epoch, offering a potential avenue to address certain observational discrepancies related to the structure formation process. Then, we constrain the parameter space of the model using recent observational datasets. Remarkably, we find that the current shear is precisely constrained to be approximately $Σ_0 \approx - 10^{-4}$. We also discuss some key differences in the expansionary dynamics sourced by the 2-form field compared to a 1-form field, i.e., a vector field, offering insights into their respective impacts on the support they provide to late-time anisotropy.