A multibasic algebra \((M,\omega)\) is defined as a special case of a heterogeneous algebra, i.e. it is \((A_1,\dots, A_n,A_0,\omega)\) where \(A_i\in M\) are nonempty sets and \(\omega\) is a mapping from \(A_1\times\cdots\times A_n\) into \(A_0\). A congruence is an equivalence \(\varepsilon\) on \(M\) satisfying the condition \[ \omega([a_1]\varepsilon(A_1),\dots, [a_n]\varepsilon(A_n))\subseteq [a_0]\varepsilon(A_0). \] The set of all such congruences need not form a lattice with respect to a natural ordering. The author studies maximal subsets of congruences which determine the whole set of these congruences. The majority of results is formulated for multibasic algebras derived from groups and quasigroups.