Max, which has headquarters in London, said it started drilling a new appraisal well in the Uytas field in Kazakhstan. The company said the latest well is the third of 13 planned for the field.
The company reported Monday it made an oil discovery in the same reserve area after drilling to a depth of 1,475 feet onshore. The company said the discovery measured 36 feet thick.
An April report from Max estimated the field's reserve potential at 778 million barrels of oil.
Kazakhstan hosts the Kashagan oil field, one of the largest in the world, with as much as 16 billion barrels of estimated commercial reserves.
Amnesty International last week expressed concern about the human rights situation in Kazakhstan. Kazakh authorities last year charged demonstrators involved in 2011 clashes in the western oil city of Zhanaozen with plotting to overthrow the government. At least 15 people were killed during labor strikes in the city two years ago.