Landbridge's first offer, made public on March 10, involved the acquisition of all of WestSide's ordinary shares at 36c per share, an offer that WestSide rejected.
The new bid has upped the stakes to 40c per share, made through Landbridge's Australian subsidiary, and follows hot on the heels of a mass share buy-up by the company last week, giving it a 19.99% interest in WestSide.
"To date, WestSide has not allowed Landbridge to conduct customary due diligence investigations and WestSide has not been willing to engage in any meaningful discussions around our indicative offer price, hence we have respectfully decided to put our proposal direct to shareholders, a number of whom have already agreed to sell to Landbridge," Landbridge said in a statement.
"Landbridge remains open to having constructive discussions with the WestSide board and given the strong shareholder support and the compelling premium implied by our new takeover bid remains hopeful the board will recommend our new takeover bid."
Landbridge said the new offer was less conditional than the initial one, with no defeating conditions applying to the actual making of the takeover bid.
WestSide has continued to recommend that its shareholders take no action while its board considers the new offer.
A final recommendation is expected in a target statement to be issued in due course.
WestSide has also noted the decision by its shareholder Energy Infrastructure Trust to sell the majority of its holding to Landbridge.
WestSide director John Clarke is also managing director of Infrastructure Capital Group, which manages EIT. However, WestSide asserted that a separation of roles meant that Clarke was not aware of, and had nothing to do with, EIT's sale of its shares.
Highbury Partnership Limited and Allens have been respectively appointed as WestSide's financial and legal advisers on the offer.