Assuming by "African" you are thinking of rift lake cichlids, then the answer is no, you cannot combine those with any other cichlids (and very few other fish for that matter). The African rift lakes contain water high in minerals (hardness) and alkalinity (pH), Lake Tanganyika for instance has a pH close to or perhaps exceeding 9 and Lake Malawi is up to 8.6 so the fish that are endemic [means they occur no where else on earth but evolved within these lakes] to these lakes require water that is much harder and alkaline that that suitable for most other fish.
By contrast, the cichlids from South America are for the most part soft acidic water fish, though a few species do occur in slightly basic water but the hardness is no where near what it is in the rift lakes. Central America also has some similar-water species.
However, if by "African" you actually meant the dwarf cichlids from the soft acidic water areas of West Central Africa, like for example the several species of Nannacara, Anomalochromis and Pelvicachromis (the familiar "Kribensis
" is a Pelvicachromis species), then these could be maintained in aquaria with certain of the American cichlids. Such a large grouping of fish means certain species have specific behaviour traits and one has to ensure compatibility, but at least the water parameters are close.