Prosecutors have asked a Norwegian court to hand Marius Borg Høiby a prison term of seven years and seven months, saying he should be convicted on 39 of 40 charges brought against him.
Høiby, 29, faces four counts of rape and a charge of serious assault among a wider slate of accusations.
He denies the most serious allegations, saying sexual encounters with the four women were consensual.
The case has been heard in Oslo district court for almost seven weeks and has dominated headlines across Norway.
Judges are expected to retire this week to consider their verdict after closing arguments.
State prosecutors told the court that three of the alleged rapes merit two-year sentences and the fourth a three-year term, and noted evidence that in three incidents women were filmed while incapacitated.
Police say the women were asleep or otherwise unable to consent when intercourse occurred.
Høiby has admitted to several lesser offences, including a drugs charge tied to transporting 3.5kg of marijuana, traffic violations and breaching a restraining order.
He has also partially admitted one count of serious assault.
His defence team has denied the most serious charges and was due to present its closing arguments later.
Prosecutors argued that earlier consensual relations do not excuse the alleged conduct and urged the court to treat the abuse and rape accusations as grave crimes that can have long-term consequences for victims.
The defendant has spoken openly about the intense media scrutiny, saying the coverage has transformed how he is viewed.
The trial began at a time when his mother, Crown Princess Mette-Marit, was also under public scrutiny over past contacts with the late Jeffrey Epstein.
Observers say Høiby could receive a reduced overall sentence because he has pleaded guilty to several lesser offences, with the drug transport charge alone carrying a potential sentence of about 11 months.
The court will hand down its decision after the judges finish deliberations.
