In a move that is bound to anger member firms, the SIB wants the new breed of registered principal traders - who are to replace market-makers - to be given a wider role in supporting the dealings of the market as a whole.
But the Stock Exchange, backed by member firms, is strongly resisting a change to its plans.
Kenneth Clarke, the Chancellor, made clear last month that he would have to be satisfied on this public interest aspect of the reforms before he gave away taxpayers' money to the Exchange's members in the form of continued stamp duty relief on share transactions. At stake is hundreds of millions of pounds of relief each year.
SIB officials believe that the plans announced by the Stock Exchange last month may not meet the main criterion for relief, which is that the firms that receive it are benefiting the liquidity of the market as a whole.
The Chancellor has asked the SIB, chaired by Sir Andrew Large, to make recommendations early next month on how the restructured stock market can qualify for tax relief.
But at the Stock Exchange the new plan represents a compromise after three years' argument among member firms and there is reluctance to alter it.
The disagreement between the SIB and the Exchange about the registered traders centres on the key issue of whether the traders deal on or off the main market.
The registered traders would swing into action whenever the new electronic order book system of trading - on which buyers and sellers are automatically matched - cannot cope, because orders are too large. They are an essential mechanism for keeping the market going.
Under the Exchange's proposals, the traders would deal bilaterally on large blocks of shares by telephone with their own customers or with other Stock Exchange member firms.
The Exchange's big members are said to prefer this because it is more cost-effective to devote capital to trading with their own approved customers rather than any investor who calls up to buy or sell. However, the SIB is trying to steer the Exchange away from this off-market telephone trading of large orders. It is looking for a system in which the registered traders are more closely linked to the main electronic order book, giving greater liquidity and openness to the market as a whole.
This set-up would make it easier to recommend giving stamp duty relief on the Chancellor's terms. SIB officials believe this method, used by the Tradepoint dealing system, may not be transferable to the Stock Exchange, but weeks away from the deadline for recommendations they are continuing to search for a compromise closer to their ideal.
One compromise floated by the SIB would be to insist that the registered traders are obliged to deal with all users of the electronic order book.
But when large blocks of stock are not available on the electronic screens all users of the order book would be entitled to make a phone request to a registered trader for a quote.
SIB officials acknowledge that there is no point in insisting on a system that the Stock Exchange cannot operate, but with stamp duty at stake they have a substantial carrot to persuade the Exchange to modify its proposals.