Identification strategies are discussed for Structural Vector Autoregressions (SVARs) which combine the use of external instruments, the so-called proxy-SVAR or SVAR-IV approach with the heteroskedasticity found in the data, the so-called identification-via-heteroskedasticity approach. The focus in on the case in which r valid instruments are used to identify g>=1 structural shocks of interest, with r>=g, and there are m structural breaks in the VAR error covariance matrix which give rise to m+1 volatility regimes. It is shown that the combination of the two approaches enhances identification possibilities for practitioners and produce overidentified testable models, denoted HP-SVARs. Two types of heteroskedasticity are considered. In one case, the structural breaks do not affect the on-impact coefficients so that the Impulse Response Functions (IRFs) are constant across volatillity regimes. In the other case, the structural breaks affect the on-impact coefficients and thee IRFs are regime-dependent. General identification results for HP-SVARs are derived for these two cases. Estimation can be carried out through maximum likelihood.