The goal of fairness in classification is to learn a classifier that does not discriminate against groups of individuals based on sensitive attributes, such as race and gender. One approach to designing fair algorithms is to use relaxations of fairness notions as regularization terms or in a constrained optimization problem. We observe that the hyperbolic tangent function can approximate the indicator function. We leverage this property to define a differentiable relaxation that approximates fairness notions provably better than existing relaxations. In addition, we propose a model-agnostic multi-objective architecture that can simultaneously optimize for multiple fairness notions and multiple sensitive attributes and supports all statistical parity-based notions of fairness. We use our relaxation with the multi-objective architecture to learn fair classifiers. Experiments on public datasets show that our method suffers a significantly lower loss of accuracy than current debiasing algorithms relative to the unconstrained model.