Kazakhstan is partly European (but mainly Asian). For the Caucasian nations, the border between Asia and Europe is being discussed. Cyprus is often heavily disputed in this forum, but in the quizzes it is almost always considered Asian. Israel is definitely Asian (the only undisputed country in this quiz). Other candidates would be Russia (which is almost always considered a European country) and Turkey (which ist mostly considered an Asian country).
The Caucasian nations are generally considered to be in Asia, so I will keep them on here. You raise a good point about Turkey, I completely forgot to add them to this list. Russia is definitely in Europe, most of the population lives in the European part but very few in the larger Asian part.