We describe the roles of multiple electronic continua in high-harmonic generation from aligned molecules. First, we show how the circularity of emitted harmonics tracks the interplay of different electronic continua participating in the nonlinear response. Second, we show that the interplay of different continua can lead to large variations of harmonic phases. Finally, we show how multiple electronic continua allow one to shape the polarization of high harmonics and attosecond pulses.