interface EventEmitter<Mapping> {
    on<EventName extends keyof Mapping>(eventName: EventName): void;
}

interface PayloadA {
    readonly foo: number;
    readonly bar: string;
}

interface PayloadB {
    readonly foo: number;
    readonly baz: boolean;
}

type EmitterA = EventEmitter<PayloadA>;
type EmitterB = EventEmitter<PayloadB>;

interface ModuleA {
    readonly type: 'a';
    readonly on: EmitterA['on'];
}

interface ModuleB {
    readonly type: 'b';
    readonly on: EmitterB['on'];
}

function doStuff(mod: ModuleA | ModuleB): void {
    if (mod.type === 'a') {
      mod.on('foo'); // works
    } else {
      mod.on('foo'); // works
    }
    mod.on('foo'); // doesn’t work
}