Orthodox quantum mechanics violates ‘value definiteness’, whereby all observables for a given particle or system at a time have precise values. This indeterminacy (reflected in, e.g., position-momentum duality and the incompatibility of joint spin-component values) is supposed to be metaphysical rather than epistemic or semantic; but can we make sense of quantum metaphysical indeterminacy (quantum MI), and if so, how? Here I consider the prospects for doing so associated with two recent approaches to MI. On a ‘meta-level’ approach, MI involves its being indeterminate which determinate state of affairs obtains; this approach has been implemented in, e.g, Akiba 2004 and Barnes and Williams 2011 as a form of metaphysical supervaluationism. On an ‘object-level’ approach, MI involves its being determinate (or just plain true) that an indeterminate state of affairs obtains; this approach has been implemented in Wilson 2012 as involving an object’s or system’s having a determinable property, but no unique determinate of that determinable. I first provide needed further support for arguments in Darby 2010 and Skow 2010 according to which a meta-level metaphysical supervaluationist approach cannot accommodate quantum MI, due to incompatibility with the Kochen-Specker theorem; here also I raise a classical analogue to the Darby-Skow concern. I next motivate my object-level determinable-based account of MI, then draw on and respond to discussions in Bokulich 2014 and Wolff 2015 to argue that either a gappy or glutty implementation of a determinable-based account can accommodate quantum MI.