How to I explain to my client that having a different logo for every event undermines their brand?

I'm a design graduate working freelance and I've designed a logo for a client who hosts a number of events: has a radio station, club night, band nights etc.... They want a completely different logo for each of these and I am struggling a little on how to explain that this is not a good idea as it undermines the continuity of the brand for recognition by customers etc. I feel that a slight variation of the logo, perhaps the colours etc would be a better idea. For example Coca Cola which keeps it bright red but uses abbreviations 'Coke' and adds 'Zero' on other products. Can anyone tell me some other examples and how to explain this to them? Thanks