They believe if they can gain a 5% holding, then they can have a real say in the running of the Glasgow giants.
BuyRangers, the fan ownership scheme run by Rangers Supporters Trust (RST), bought another 200,000 shares in the club this week.
They bought 357,856 shares for £250,000 when Rangers held an initial public offering (IPO) in December 2012.
This latest outlay, which was made possible after fans pledged £52,000 via direct debit, takes their holding to 557,856.
BuyRangers still have only a 0.86% stake in the SPFL League One leaders. However, Trust officials are hopeful they can snap up more, due to the share price tumbling from 70p to below 30p. And hopes are high fans can eventually achieve board representation.
RST chairman Gordon Dinnie said: "We started our direct debit scheme just before Christmas. If we can get enough interest going in that, then we can buy shares on a monthly basis and build up our stake. We can also borrow against that money coming in and use it to buy more.
"However, the big issue is availability of shares. With the current price being so low, when you try to buy them on the market folk are asking for a few pence more. So it's not a case of buying £1million-worth of shares if there is £1m-worth available.
"We don't need to aim for anything like a 50% stake. Because of the fractious nature of the shareholding, a 10% stake could give you a major say in how the club is run.
"James Easdale had just one more share in the club than the RST after the IPO yet he was appointed to the board.
"If we get to 5%, we would hold the right to call a general meeting, and the things you are able to do increases as your stake goes up.
"We need to take it slow but if we can generate enough interest then we can look towards taking our holding past 1%, then 5%. As our stake in the club grows we can think about getting a director on to the board - elected by the fans."
Dinnie refused to condemn the prospect of another group of Rangers fans starting up a Community Interest Company - the way Hearts fans bought the Tynecastle club.
Supporters Direct Scotland will host a meeting in the Louden Tavern tomorrow to advise Rangers fans about how they can go about setting up a CIC
Dinnie said: "They say their meeting is a consultation process and not a new scheme, so there is no need for us to stop doing what we're doing. In fact, we're now cracking on with BuyRangers.
"The long-term aim is to see fan ownership realised at Ibrox. Their new scheme could have worked alongside BuyRangers.
"However, I won't condemn it. It would be ludicrous for me to condemn it when they are working towards the same thing as we are.
"We will carry on with BuyRangers because we think it is the best way forward."