There are many approaches to paraconsistency, ranging from the very moderate to the more radical. In this talk I will explore and extend the more radical end of the spectrum, where there are truth-value gluts. The aim is to evaluate the philosophical and technical tenability of such an approach. The strategy is to argue that, insofar as there is good reason use a glutty theory, then there is good reason to use a glutty meta-theory too. The issue is how to go about doing so. We will look at a few examples, from semantic and proof theoretic validity, and computability. I will show that there are very significant technical challenges to face on this sort of radical approach, but that there is good philosophical support for facing these challenges.