A method is presented to automatically increase the threshold projection parameter in three-field density-based topology optimization to achieve a near binary design. Topology optimization methods aim to find where material should be placed within a design domain to meet certain constraints, whilst minimizing, or maximizing an objective. One of the most popular approaches for solving this problem is to use pseudo-densities, where the material existence design variables (typically defined element-wise) are relaxed to be continuous between 1 (solid) and 0 (void). However, this can lead to intermediate pseudo-density values in the solution (especially when filtering methods are employed), which may be difficult to interpret for manufacturing. A popular approach to achieve near binary designs with continuous pseudo-density values is to use a smooth threshold projection function that pushes the physical pseudo-densities close to binary values (1 or 0). The sharpness of the projection function is controlled by a projection parameter. From experience, researches usually start with a small value of this parameter, which is incrementally increased during the optimization - usually referred to as a continuation scheme. This allows a design to emerge in the early iterations, whilst being projected close to a binary design at the end - e.g. [1, 2]. However, this is usually done ad-hoc with manual parameter tuning for different problems. In this work, an automated procedure for increasing the threshold projection parameter during optimization is explored. Parameter increase each iteration is based on information about optimization progress. This results in a method that does not need to be tuned for specific problems, or optimizers, as the same set of hyper-parameters can be used for a wide range of problems. The effectiveness of the method is demonstrated on several benchmark problems, including challenging linear buckling, and geometrically nonlinear problems. [1] F. Ferrari and O. Sigmund, A new generation 99 line Matlab code for compliance topology optimization and its extension to 3D. Structural and Multidisciplinary Optimization, Vol. 62, pp. 2211-2228, 2020. [2] P. Dunning, Stability Constraints for Geometrically Nonlinear Topology Optimization. Structural and Multidisciplinary Optimization, Vol. 66, 253, 2023.