No. There is the Focus Target feature, but that would be more effort for each target and only show you the first six or so effects. I do enjoy using it when I want to see casts and effects on a monster that won't always be my target in raids and such ... but no, at present, the buffs and debuffs both are inextricably stuck under the target's health bar.

There's also a setting to show only the effects you can actually do something about to more easily spot your own amidst the clutter of less relevant effects. I don't use it personally because I can pick out the green text easily enough (which indicates it's my effect). But it would at least offer you the option of showing fewer effects there.