Police had previously investigated a complaint about Falloon sending an unsolicited image at the beginning of July but it wasn't found to meet the threshold for prosecution.
Today a further three women have come forward and Falloon, 37, quit as Rangitata MP.
The now-disgraced ex-MP had previously said he would resign at the election, after news of him sending pornography to a young woman first hit headlines last night.
Since then, more women have come forward saying they too have received inappropriate material from Falloon – Collins said two have already been in contact with her office this morning.
Speaking to media this morning, Collins said she was "sorry to say I believe we are going to have more women come forward".
"If I've had two come into the office already this morning, there will be more."
Collins said Falloon had been caught out in an "enormous lie" which was why getting to the bottom of his behaviour was a "drawn out process".
"He's been lying and that's the problem. The one thing about liars is you never actually know that they're lying until you've got the information otherwise. If someone tells me quite firmly, 'these are the facts' then I am obliged - unless they have contrary information - to accept that."
Collins said when she spoke to Falloon on Monday, she asked whether there was anything else they should know about.
"We were told 'no'. That's an enormous lie and one that goes to the heart of whether or not I could trust him as an MP and so he's gone."
Collins said she'd told a white-lies about trivial matters - like telling someone they looked nice in a jacket - "but not on serious matters".
Collins said she made it clear to MPs in their caucus this morning what her expectations were of them and everybody had been given the opportunity to come forward if they knew anything more. She said they were all "utterly shocked" by Falloon's actions.
"I was very, very clear as to my expectations. I told them to accept the privilege of being an MP and that I expect them to act in a professional manner that this is not the sort of thing that people expect from their MPs or anyone else in a privileged position."
Falloon's parents said today they were "shattered" over his sex-text scandal and are yet to speak to him.
John and Shirley Falloon - who live in Ashburton in mid-Canterbury, in the heart of Falloon's old Rangitata electorate - have been rocked by this week's revelations.
John Falloon told the Herald today that he only knows what is being reported in the media.
"I haven't had a chance to have a yarn with Andrew yet," he said.
"He's not well at the moment and we're just seeing him through that."
John Falloon was confident that his son was getting appropriate support.
"We're just trying to keep him protected at the moment," he added.
"It's been pretty shattering. But life has these wee surprises."
