we define and investigate new classes of almost 3-contact metric manifolds, with two guiding ideas in mind: first, what geometric objects are best suited for capturing the key properties of almost 3-contact metric manifolds, and second, the newly defined classes should admit ’good’ metric connections with skew torsion with interesting applications: these include a well-behaved metric cone, the existence of a generalized killing spinor, and remarkable curvature properties. this is joint work with giulia dileo (bari) and leander stecker (marburg).