At day mostly single engined planes were used, like Me 109 or FW 190. At the first time also heavy fighters like the Me 110, Ju 88 and even the He 177 Greif heavy bombers were used as interceptors and rocket platforms. They had some success but were withdrawn after more and more fighters came, as they had nearly no chance. Later the only plane with more than one motor was the Me 262 jet.
However since you are interested in this a story of the German night fighter ace, Hans- Joachim Jabs, 50 victories (28 night, 22 day):
Jabs was flying at day his Me 110 night fighter to his base. I don´t remember why, but he flew at day. Over his base he suddenly met 8 Spitfire Mk IX! Jabs avoided the first attack and took a position behind the last Spitfire. His guns shot the plane to pieces. The British were surprised and Jabs tried to reach his base. The British followed him and again he could evade and shoot down the next enemy.
I should say he shot down in the Battle of Britain 8 Spitfire and 4 Hurricane with his Me 110 at day, so this was nothing really new for him, and he was an ace. However he had to think also about his crew so he decided to land and to scrifice the plane, when the British hit him for the first time.
He managed to land somehow with big damages. He and his crew could just cover, when 3 British planes finished off his Me 110. However the British lost two planes against an enemy, which was by far no fighter killer.
Adler