I have a graduation cake order. It will have both the high school and college logo on the cake. One logo is royal blue and gold, the other is navy blue, kelly green, and gold......How can I make these colors mesh...Two tier cake. Would white be the best base color for the cake you think? I feel like the blues are going to clash and just look like I don't know what Im doing.

white or chocolate for base cake -- yes and if you put a base under each logo so they both stand out on a white or black background -- in the shape of the logo -- like you did the bulldog -- the red dog on the white background -- it would help bring them together -- but it will make sense to the honoree/s and that's what counts -- get them about the same size of course and you're golden -- you could do all the decor in white (chocolate) so the logos are the stars --

or you could do a banner that curls up on each end like a wide ribbon stretched across the cake and put both logos on that -- or mount them on plaques

brainstorm type ideas for you

Something that helps when making flowers might help here.  Add a tiny bit on one color to the other.   In other words mix a bit of kelly green into the blue and a bit of blue into the green.  It doesn't take much but makes the colors 'mesh' w/o muddying the waters so to speak :)

I like k8's suggestion of backing the logos w/white or hey maybe gold - that might be a way of getting the gold color into the whole scheme especially if you are icing the whole cake in white.

My school colors (back in the **OLDEN** days - 60 yrs ago) were B & G.  The 'gold' is really a dark yellow w/a tiny touch of brown rather than shiny gold.