The 46-year-old was last seen at Cross Lane Hospital in Scarborough on the evening of Wednesday May 8.
The most recent sighting, which has not been ruled out, was near Scarborough Road roundabout in Bridlington and CCTV cameras are currently being reviewed.
Faye Noble, friend of the family, said: "Pete's been missing over nine-weeks now.
"There have been lots of possible sightings across East Yorkshire, however he really could be anywhere.
"Please continue to keep an eye out for him, check places he could seek shelter, and keep an eye out for any new homeless people in the area.
"Everyone's help and support is hugely appreciated, if anybody feels they can help in anyway or you would like more information please get in touch with us on our dedicated Facebook search group."
As part of a huge community response the group - Pete Brown Search & Updates - has been set up to share new information and events of planned searches in the area.
Peter, from Whitby, is described as white, about 6ft 1in tall, of muscular/athletic build, unshaven with greying/brown hair which is slightly thinning.
He was last seen wearing a blue waist length jacket with a blue hoodie underneath, loose grey cotton jogging bottoms, and blue Nike trainers.
It is believed that he could also have been wearing a blue baseball cap and may have changed into blue jeans.
However, police believe he may be sleeping rough so his appearance may be more dishevelled than in pictures.
He has also been listed on the Missing People website.
"If you do come across somebody you think is Pete, please take a discreet picture, keep him in sight and ring North Yorkshire Police (999 if you are sure it's him). I can not stress this enough, we could rule all sightings in or out with a simple picture.
"Thank you for everyone's continued help and support at this extremely difficult time, the general public have been amazing," she added.
Anyone with any other information about Peter's whereabouts is asked to contact police on 101 and quote reference number 12190083137.