Forensic tests are being carried out on remains and tools found in the River Aire by police searching for the bodies of two Bradford women.
Stephen Griffiths has been charged with murdering prostitutes Suzanne Blamires, Shelley Armitage and Susan Rushworth.
Only Ms Blamires' body parts have so far been found. Remains pulled from the river on Saturday are being tested to find out if they are human.
A large suitcase later pulled from the river contained tools, police said.
Mr Griffiths, 40, gave his name as "the crossbow cannibal" in court on Friday. He is due to appear at Bradford Crown Court again via videolink from Wakefield Prison on 7 June.
Police found 36-year-old Ms Blamires' body parts in the River Aire near Shipley on Tuesday. They found more remains about 200 yards away in the river on Saturday.
Police said as far as they were aware all of Ms Blamires' remains had been recovered.
The mood outside the block of flats where Mr Griffiths' lived was described as strange as residents sign in and out each time they go anywhere.
A pile of flowers has been steadily growing outside the building over the weekend.
Elsewhere, detectives knocked through a wall before sifting through the sand and soil which came out of it with a trowel.
Forty-five detectives are now working on the case with support from about 70 other officers.
Ms Armitage, 31, has not been seen since 26 April and Ms Rushworth, 43, has been missing for almost a year.
Police have been conducting fingertip searches across the city, including in the drains around Mr Griffiths' Thornton Road flat.
Legal brothel call
Floral tributes have been tied to railings next to the river, which has been sectioned off from the road with police tape.
A West Yorkshire Police spokeswoman said: "Officers are continuing to search areas of Bradford city centre and the River Aire throughout the day and are also proactively following several lines of inquiry.
"This will continue throughout the Bank Holiday and into next week."
She said tests were continuing on the remains found in the river, adding: "At this stage it is unclear whether they are human or animal."
Meanwhile, Philip Davis, Conservative MP for Shipley, has called for brothels to be legalised.
He said: "I think there is an argument for getting these women indoors where they will be off the streets and in relative safety."
He said he would be contacting other MPs to see how much support there was for his plan.
Prime Minister David Cameron has already said that the decriminalisation of prostitution should be "looked at again" following the deaths.