The detection of the electric network frequency (ENF) in digital recordings is an essential step before the subsequent ENF extraction and forensic analysis. In this letter, we extend the state-of-the-art single-tone time-frequency (TF) domain ENF detector to the multi-tone scenario and propose a multi-harmonic combining (MHC) method, exploiting ENF harmonic components for improved detection performance. To exclude the corrupted components interfering rather than contributing to ENF detection, the proposed detector first performs a pre-screening based on the estimated average subband signal-to-noise ratios (SNRs) to exclude interfering components. Then, with the selected harmonic candidates, a second screening process is applied based on the TF test statistics (TSs), i.e., the variances of observed subband traces. After that, the multi-harmonic components are combined to form the final TS, whose sign determines the final decision. The advantages of the proposed method are illustrated via both synthetic analysis and real-world experimental results using the ENF-WHU dataset.