Maxim and Quest already have a well-documented relationship and were involved in a proposed new venture in the United Arab Emirates, but that deal was subsequently cancelled in August due to lack of financing.
QE is part of the Quest Group which includes Quest Investment LLC and Quest Oil & Gas Ventures Inc.
Today's co-operation agreement will see the firms consider production or near term production opportunities, "which may include strategic opportunities that could be considered unconventional but can lead to an expanded asset or set of opportunities", said Maxim.
"The parties intention is that cash flow or near term cash flow will be a strong focus for the opportunities considered under the terms of the agreement," it added.
Andrew Male, Maxim's chief executive, said: "This agreement provides a unique opportunity for Maxim to be able to access projects that it may normally not be able to.
"The agreement also enables Maxim to have continued access to the technical expertise of Quest and its affiliates.
"In turn, we believe that Maxim's public company platform will provide access to the capital markets for necessary financing for opportunities which arise under the Agreement.
Overall, we believe that the agreement solidifies Maxim's strategic relationship with Quest and we look forward to continuing to working with Quest."