By the time of the D-Day landings the Russians had expelled the Germans from the whole of the Soviet Union and were racing into Poland and the Balkans. By this rate of advance it was evident they would overrun all of eastern europe by the following winter - as indeed they did. This horrified Churchill. He understood exactly what Stalin was. Churchill pressed for an immediate invasion of Germany to bring about an early surrender and thus halt the progress westward of the Soviet armies.
This desire produced the Anglo-American airborne invasion of the the lower Rhine crossings at Arnhem in September. An attempt at a lightning strike across the north German plain to capture Berlin. Unfortunately it was defeated and so in October Churchill flew to Moscow in the hope that the diplomacy of realism could secure what the paratroopers had failed to win.
At a meeting with Stalin in the Kremlin on 9th. October Churchill asked him directly "How would it do for you to have ninety percent predominance in Rumania, for us to have ninety percent of the say in Greece, and go fifty-fifty about Yugoslavia?"
Churchill sketched out these figures on paper, adding 50-50 for Hungary and 25-75 Bulgaria. Stalin "took his blue pencil and made a large tick upon it, and passed it back to us". Stalin also agreed that after the war Britain would be the leading Mediterranean power.
Notice - significantly - that there was no mention of Germany, Czechoslovakia or Poland? Churchill understood they were lost. There would be no practical way of preventing Soviet occupation in 1945 just as there was no practical way to stop the German occupation of 1939. However, Greece was saved from Soviet occupation, Yugoslavia was allowed to go its own way and the threat of Soviet influence upon the immediate post-war politics of Italy was removed.
Could he have done more? Its difficult to see what else he could have done.