Dhaka Chief Metropolitan Magistrate (CMM) Court allowed the petitions filed by Paltan police to that end.
The three investigations officers of the cases also appealed for 30-day remand to question the BNP leader.
Sub-Inspector Aminur Rahman, general recording officer (GRO) of CMM court, told bdnews24.com that the hearing on the remand petitions will be held on Wednesday in the court of Magistrate Ashok Kumar Dutta.
According to the court sources, one of the three cases was filed by police on Jan 5 against Alamgir and 28 others for vandalising and torching a bus in front of Bangabandhu Hawkers Market in Gulistan.
The second case was filed against Alamgir and 49 other leaders and activists of BNP on charge of setting fire to a motorbike of a policeman in Fakirapool on Jan 5.
Another case was filed against him and 33 others for torching a BRTC bus at Purana Paltan on Jan 6.