They can start buying on market seeing as the conditions to allow them to do that have been met. However, the maximum price they can pay is 5.5c, same as the offer.
If they start buying at prices higher than that, under the off-market takeover rules, the offer price will be automatically increased to the highest price the bidders has paid on mkt.
Here's another guide (link at bottom of post) on Australian takeovers I've found to be very thorough and in layman's language even though it comes out of a lawyers office. Our situation is the off-market bid for the company
Some examples:
Duration of offer
Offers under an off-market bid must remain open for acceptance for a minimum of one month but can be extended so that the offer is open for a maximum of twelve months. The offer period will automatically be extended by 14 days if, within the last seven days of the offer period, the bidder’s voting power in the target increases to more than 50% or the offers under the bid are varied to improve the consideration offered.
Variations to bid terms
Takeover offers under an off-market bid can be varied in a number of different ways including by increasing the bid price, by extending the bid period or by offering additional alternative forms of consideration. Offers are generally varied where the bidder makes an improved offer. Variations can only be made by giving notice to the target, target shareholders and the ASIC. A variation which increases the bid price in the last seven days of the bid period will automatically extend the bid period by 14 days.
Final and best offers
Statements made in the course of a takeover must not be misleading or deceptive. Sometimes the bidder may use a bid to test market reaction, with the intention of later increasing the offer price. Any statement that the bid price is the “final and best offer” or that “the offer period will not be extended” may be considered to be misleading, if the bid price is subsequently varied or the offer period extended.
Selling down during an offer
Where a bidder’s statement has been served on the target company, neither the bidder nor any of its associates is permitted to dispose of any shares in the target during the takeover period unless they are accepting a competing takeover bid which was launched (or improved) after the bidder’s statement was served on the target company.
This is a very good document that even describes what may and may not be done between bidder, directors and major shareholders PRIOR to an offer being made for a company.