Coherentism
Coherentism accepts the regress argument's setup and rejects its picture. Justification is not a substance that flows along a chain from a source; it is a property of a whole system of beliefs that fit together — explaining each other, entailing each other, failing to contradict each other.[1] On that picture no belief is privileged and none is basic, so asking where the chain stops is asking the wrong question. Neurath's image is the standing one: we are sailors rebuilding our boat plank by plank at sea, with no dry dock to start from, able to stand on the rest of it while we replace any part.
This is not the fallacy it looks like. Circular reasoning is vicious because it transmits justification from a premise back to itself along a line; coherentism denies that justification is transmitted along lines at all. The real test is holistic and familiar from science, where a theory earns its keep by making a large body of observations hang together rather than by resting on some observation that needs no support. Note the cost, though: what makes a system coherent is more than consistency. A set of unrelated true sentences is perfectly consistent and coheres with nothing.
Two objections do the damage. The isolation objection: a well-constructed fairy tale can be as coherent as a physics textbook, so coherence alone gives you no contact with the world — the complaint empiricism would make. The plurality objection: for any coherent system there are rival systems, equally coherent and incompatible with it, and coherence cannot say which to hold. The standard repair is to require that beliefs arising from observation carry some weight of their own — at which point critics ask how that differs from admitting a foundation. Susan Haack's foundherentism accepts the hybrid on purpose, with the crossword puzzle as its image: entries answer to the clues (experience) and to how well they interlock (coherence), and neither alone settles the grid. Whether that is a third position or foundationalism with better manners is still argued.
The isolation objection can be sharpened until it bites formally. Take independent witnesses reporting on the same event; let coherence measure how well their reports agree. The hope is that agreement raises the probability that they are right — that a more coherent set is, other things equal, more likely to be true. Formal work on this has been largely negative. Bayesian treatments (Klein and Warfield's original puzzle, then Bovens and Hartmann, then Olsson) show there is no coherence measure that is truth-conducive in general: for plausible ways of making "coherence" precise, one can construct cases where the more coherent set is the less probable one.
The reason is that coherence is blind to where the reports came from. Ten witnesses who agree because they compared notes are highly coherent and evidentially near-worthless; ten who agree without contact are coherent and informative. Probability tracks the difference, coherence alone does not — which is why the surviving versions all smuggle in a second ingredient: independence, reliability of the sources, or an observation requirement. This is the same shape as the objection to foundationalism's given, arriving from the other side, and it is the best current argument that neither position works in its pure form.