Two separate transactions of one million shares were made yesterday afternoon with 20 separate trades listed by the close of play today.
Precise details of the buyers are not yet available.
It comes as chief Executive Craig Mather, club consultant Charles Green and finance director Brian Stockbridge drum up support in London for the current board amid attempts by tycoon Jim McColl to oust key figures.
Today's developments came after an overseas investor in Rangers claimed the new company has been a disaster "from day one" and called for the current board to be removed.
The institutional investor, who owns around a 1% stake in Ibrox, said the exit of two chairman in quick succession and the appointment of a new stock-broker highlighted serious issues with the inner business workings of the club.
With a stake of around 650,000 shares worth approximately £270,000, he said his concerns with the current set up were shared "very widely" among other big investors, with claims that the bid by billionaire Jim McColl to force change in the boardroom will be successful.
Rangers said ongoing talks being led in London by chief executive Craig Mather, finance director Brian Stockbridge and consultant Charles Green to secure support for maintaining the status quo were positive.
Meanwhile, the club has announced the board will decide on Tuesday whether Mr Green will remain at the club as a consultant.
The meeting was called in light of Mr Green's comments about manager Ally McCoist's performance, with subsequent claims he is to support the court case of former director Imran Ahmed which will also be discussed by Ibrox directors next week.
Fans groups have called for Mr Green to be sacked, with the strength of feeling among supporters to be considered by directors.
The institutional investor, who did not want to be named, said: "It is pretty clear that corporate governance at the club is just awful.
"Since the Initial Public Offering in December we have lost Malcolm Murray, a very well respected figure, and the most recent chairman. We have also had Charles Green step down as chief executive and reappointed as a consultant which went against the wishes of pretty much everyone.
"I have never been involved with a company when somebody brings it onto the market and in six months you replace the stock-broker. You have to ask the question why.
"When you lose two respected chairmen within six months and you change the stockbroker, there is clearly something very wrong.
"We would certainly want the majority of the current board to go and replace it with a board which has the club's best interests at heart."
Rangers has recently switched its stockbroker from highly regarded Cenkos to Daniel Stewart, which has existing links with Mr Green.
The overseas financier has had past business dealings with former club chairman MrMurray, who is aligned to Mr McColl's requisitioning of an EGM.
The financier added: "It's pretty unusual for investors to take this kind of action and getting investors to sign a letter is really tough. You don't invest in a company and within 12 months expect these kind of issues. At Rangers, it's been a disaster from pretty much day one."
Rangers remain positive that they can fend off a potentially embarrassing boardroom coup. A club spokesman said: "The meet-ings that executive directors are having in London this week have been positive and supportive."
Meanwhile, the Easdale family are looking to buy more shares in the club with brothers James and Alexander, plus his wife Gail, now having just over a 1% stake.
Easdale family spokesman Jack Irvine said: "The brothers will add to their shareholding as opportunities present themselves and are considering all options."
Earlier this week, Isle of Man hedge fund Laxey, which has had past dealings with Mr Green, bought more than two million shares in the club.