The 48-year-old victim was discovered in Tettenhall Road, Wolverhampton on Monday morning.
A 25-year-old man was arrested in Wolverhampton just before 10pm on Tuesday.
West Midlands Police said it had been granted a 36 hour court extension on Thursday morning to further question the suspect.
Four other people have been bailed while police continue their inquiries.
A spokesman for West Midlands Police said: "We have this morning been granted a 36 hour court extension to further question a 25-year-old man on suspicion of murder.
"Four other people have been bailed while enquiries continue."
Police have urged anyone with information, who have not yet spoken to officers, to come forward.
Anyone with more information can contact officers via live chat on the force's website, or by calling 101 quoting log number 1574 of 28/5/23.