  For a Markov map of an interval or the circle with countably many branches
and finitely many neutral periodic points, we establish conditional variational
formulas for the mixed multifractal spectra of Birkhoff averages of countably
many observables, in terms of the Hausdorff dimension of invariant probability
measures. Using our results, we are able to exhibit new fractal-geometric
results for backward continued fraction expansions of real numbers, answering
in particular a question of Pollicott. Moreover, we establish formulas for
multi-cusp winding spectra for the Bowen-Series maps associated with finitely
generated free Fuchsian groups with parabolic elements.
