He also received a gold medal in the individual classification, showing the best result on the 6th board.

In 1995, he achieved further successes: he single-handedly won the round-robin tournament in Aalborg (before Michał Krasenkow), took 2nd place in a strong competition in Copenhagen (behind Peter Leko, and ahead of Igor Glek, József Pintér, Curt Hansen and Jonny Hector) and triumphed (together with Dorian Rogozenco) in Lviv.

In 2002, he shared the 1st place in Legnica (together with Stanisław Zawadzki), and a year later he repeated this achievement (together with Gyula Sax) in Bratto (Lombardia).

In 2009, Andrei Maksimenko took the 2nd place (behind Viktor Erdős) in Berlin, and in 2013 he won (together with Vladimir Malaniuk) in the tournament for the Cup of the Lower Silesian Voivode in Legnica.

The highest rating in his career Andrei Maksimenko was reached on November 1, 2011, when he took 33rd place among Ukrainian chess players with a score of 2559 points.