Regexp for variable length tags

I am processing some data that has a up to three key-value pairs concatenated together. The keys can be "ADD, REM, EQD". Values are variable length.

There will always be an "ADD" section, followed by 0 to 1 "REM" sections, followed by 0 to 1 "EQD" sections. For example:
ADDxxxxxxxxREMyyyyyEQDzzzzz

I'm trying to find a regular expression that will split this apart into separarate sections in one step.

So far, I have this:

$rec =~ /(ADD.+)(REM.+)(EQD.+)/;

But, this only works if I know the record has all three tokens.

This gobbles too much:
$rec =~ /(ADD.+)(REM.+)?(EQD.+)?/;

Any ideas?

-Jon
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