Change the following sentence from active to passive: The staff might have been installing the new server last night.
The new server might have been installed last night by the staff.
Active: The staff (subject) might have been installing (verb) the new server (object) last night.
In passive voice the object 'the new server' becomes the subject and the doer 'the staff' moves into a 'by' phrase.
The verb is in the modal perfect continuous form (might have been + -ing). A strict passive would be 'might have been being installed', which is awkward and rarely used, so the accepted passive keeps the modal perfect form: might have been + past participle → 'might have been installed'.
Other choices change the modal or the tense: 'installed' stays active, 'has been installed' drops 'might' and wrongly uses present perfect with 'last night', and 'might be installed' loses the perfect sense needed for a past time ('last night').
Hence, the answer is The new server might have been installed last night by the staff.
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