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We present VLT/MUSE observations targeting the extended Lyman-α(Lyα) emission of five high-redshift (z ∼ 3-4) submillimeter galaxies (SMGs) with increasing quasi-stellar object (QSO) radiation: two SMGs; two SMGs that host a QSO; and one SMG that hosts a QSO with an SMG companion (QSO+SMG). These sources are predicted to be located in dark matter halos of comparable masses (average mass ofM_DM ∼ 10^12.2 M_⊙). We quantified the luminosity and extent of the Lyαemission, together with its kinematics, and examined four Lyαpowering mechanisms: photoionization from QSOs or star formation, shocks by galactic and/or QSO outflows, gravitational cooling radiation, and Lyαphoton resonant scattering. We find a variety of Lyαluminosities and extents, with the QSO+SMG system displaying the most extended and bright nebula, followed by the SMGs hosting a QSO, and finally the undetected circumgalactic medium of SMGs. This diversity implies that gravitational cooling is unlikely to be the main powering mechanism. We show that photoionization from the QSO and QSO outflows can contribute to power the emission for average densitiesn_H > 0.5 cm⁻³. Moreover, the observed Lyαluminosities scale with the QSO’s budget of Lyαphotons modulo the dust content in each galaxy, highlighting a possible contribution from resonant scattering of QSO radiation in powering the nebulae. We find larger Lyαlinewidths (FWHM ≳ 1200 km s⁻¹) than usually reported around radio-quiet systems, pointing to large-scale outflows. A statistical survey targeting similar high-redshift massive systems with known host properties is needed to confirm our findings.