Bosonic super-WIMPs, including pseudoscalar and vector particles, are dark matter candidates. Until now, many underground experiments searches for super-WIMPs have been performed in the mass range of a few $rm keV/c^2$ to 1 $rm MeV/c^2$. All these searches utilize the absorption process of a super-WIMP by a target atom in the detector, which is similar to the photoelectric effect. In this study, we consider another process, namely, a Compton-like process. As an example, we compare the cross-section of a germanium atom for the absorption process with that of a Compton-like process. Our findings indicate that the cross-section for the Compton-like process becomes dominant, compared to that for the absorption process for mass above approximately 150 $rm keV/c^2$ for both pseudoscalar and vector super-WIMPs. In particular, the cross-section for the Compton-like process for a vector super-WIMP becomes increasingly greater than that for the absorption process by an order of magnitude to two orders of magnitude in the 400 $rm keV/c^2$ to 1 $rm MeV/c^2$ mass range, respectively. By including the Compton-like process, which has not been used in any other super-WIMP search experiment, the experimental upper limits can be improved.
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