Yang Huang, Timothy C. Beers, Kai Xiao, C. Mendes de Oliveira, Felipe Almeida-Fernandes, G. B. Oliveira Schwarz, Young Sun Lee, Jihye Hong, Huiling Chen, Huawei Zhang, Guilherme Limberg, Maiara S. Carvalho, P. K. Humire, André Luiz Figueiredo, Bruno Dias, Alvaro Alvarez-Candal, Marcos Fonseca-Faria, A. Kanaan, T. Ribeiro, W. Schoenell, Silvia Rossi

We combine narrow/medium-band filter photometry from the Southern Photometric Local Universe Survey (S-PLUS) DR4 with ultra broad-band filter photometry from Gaia EDR3 to derive fundamental stellar parameters ($T_{\rm eff}$, $\log g$, [Fe/H], ages) and elemental-abundance ratios ([C/Fe] and [$α$/Fe]) for 5.4 million stars in the Galaxy (4.9 million dwarfs and 0.5 million giants), as well as for over 0.7 million red giant stars in the Large and Small Magellanic Clouds (LMC and SMC). The precisions of the abundance estimates range from 0.05-0.10 dex for metallicity in the relatively metal-rich range ([Fe/H] $> -1.0$) to 0.10-0.30 dex in the metal-poor regime ([Fe/H] $<-1.0$), 0.10-0.20\,dex for [C/Fe], and 0.05 dex for [$α$/Fe]. The stellar parameters for LMC and SMC member stars are somewhat less precise than those from the S-PLUS main survey, primarily because of the effect of high reddening. The use of both metallicity- and carbon-sensitive filters provides unbiased measurements of both [Fe/H] and [C/Fe], of particular importance for very low-metallicity ([Fe/H] $< -2.0$) stars, where carbon enhancement can lead to systematically high estimates of [Fe/H] when only a single metallicity-sensitive filter is employed. Furthermore, multiple narrow-band filters enable metallicity estimates down to [Fe/H] $\sim -4.0$ with an accuracy of around 0.3 dex, exceeding the precision typically achieved by low/medium-resolution spectroscopy. This extensive photometric dataset, combined with the other three datasets in this series, will serve as a valuable legacy resource for Milky Way and Magellanic Clouds studies.