Three men, aged 39, 42 and 54, were arrested overnight on Friday and Saturday and a fourth was already in custody.
Police say they are not yet in a position to identify the victim.
Witnesses or anyone with information are asked to call North Yorkshire Police on 101, select option 1, and speak to the Force Control Room.
If you would prefer to remain anonymous, contact Crimestoppers on 0800 555111.
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Please quote reference number 12160190924 when providing details about this incident.
The arrests follow the death of a 50-year-old man in Scarborough.
The incident, which occurred at a flat on Princess Street, in the Old Town area, was reported by the ambulance service at 4.39pm on Thursday.
A 54-year-old local man has been arrested on suspicion of murder.
He is being held in custody for questioning while enquiries continue to establish the full circumstances surrounding the incident.