Sure, some of them could be kept, all of them would be very hard to keep. Colonies at one time were seen as morally correct and profitable, the more modern view is that they are immoral and money losers. A list of things that would help in rough order.
1) A belief that white men are morally superior to brown/black men among the general population. To some extent, Europe lost its will to keep the colonies. South Africa was able to keep attached black colonies for decades after the Europeans started to shed colonies.
2) No WW1. And stopping it just in 1914, Europe needed to find a solution that was fair enough to stop pushing so close to war every few years. Europe is much stronger in this scenario, and has much larger immigrant population. And Europe is bankrupt and exhausted after the war.
3) Changes in policies that steer European immigrants to each countries respective colonies. The higher % of people in a colony from the home country, the easier the colony is to keep. WW1 helps a lot by not stopping the mass outflows of Europeans.
4) A way to deal with new players that want Colonies such as Germany, Italy, Japan, etc. This would involve some swapping of colonies and/or allow new colonies to be made. For example, Germany either gets its Greater middle Africa Colony, Germany gets the Yangtze river basin, or something else large enough to absorb the German population outflow. Italy will also need something to absorb the outflow and merely Tunisia and Libya are too small. Maybe as a partly ASB, but the most stable situation is where the white colonist in each country are from the country that control the colonies.
5) The USA has fears about having markets, and stirred up issues. America often supported Colonial independence, so this needs to be handled. Maybe something like a formal recognition of an American Sphere of influence in part of Latin America in exchange for an American acceptance of the Colonial structure.
6) Ethnic issues in Europe need to calmed down. Promotion of ethnic minorities in other European powers just provides a moral frame work for colonies later to use against the European.
Changing any one of this would be possible, especially if only partially. To change all of them simply means we live on a different planet. I tried writing a partial sample time line, but it quickly got ASB. But in broad terms, without WW1 or another great European war I could see the following colonies surviving.
1) Russia still has Central Asia. To me, Central Asia looks like colonies attached to Russia, but some may not see it that way.
2) Japan. Taiwan, and Korea is possible.
3) UK. India is way to big to keep and the dominions are largely independent by 1910, but the UK cold keep some smaller Areas. Singapore, Hong Kong, Suez Canal Zone, Malta, Cyprus are plausible.
4) Italy: Libya as a Colony, especially if oil is found early enough and the Italian government encourages Italians to move to Italy.
5) France. A stronger France keeps Algeria and perhaps a bit more of north Africa.