We present, to our knowledge, the first theoretical realization of an independent charge-4e phase in a two-dimensional classical array of conventional superconductors coupled through altermagnetic junctions. Tuning the altermagnetic splitting suppresses the leading single-pair tunneling harmonic while retaining strong double-pair coupling, producing a finite charge-4e region between staggered and uniform charge-2e states. Using the complete temperature-dependent microscopic Josephson spectrum, we find short-range ordinary pair correlations alongside algebraic coherence of pairs of Cooper pairs. Berezinskii–Kosterlitz–Thouless scaling and a half-flux response further identify the charge-4e phase. Our results establish altermagnetism as a microscopic means to select between ordinary and composite superconducting coherence.