Officers were called to an address in Bryn Heulog, Old Colwyn, at 20:30 GMT on Thursday. David Kingsbury, 35, was found dead nearby.
Two 30-year-old men and a 50-year-old man have been arrested on suspicion of murder and are being questioned.
A 38-year-old woman arrested on Thursday has been released on bail.
A post-mortem examination revealed Mr Kingsbury died from a single stab wound.
In a tribute, Mr Kingsbury's family said: "David was a very loving, affectionate son, brother and uncle with a good heart.
"We all loved him to bits and will miss his happy, easy going nature, his infectious smile and sense of humour."
Three more people have been arrested following a fatal stabbing in Conwy county.