Took a dip, evenly spread, having too much on one's plate (7)
I believe the answer is:
swamped
'having too much on one's plate' is the definition.
(both can mean having too much to do)
'took a dip evenly spread' is the wordplay.
'took a dip' becomes 'swam' (take a dip can mean to swim).
'evenly' indicates alternate letters (the letters in even-numbered positions).
The alternate letters of 'spread' are 'ped'.
'swam'+'ped'='SWAMPED'
(Other definitions for swamped that I've seen before include "overcome" , "Inundated in quagmire?" , "Pew's mad (anag) - overwhelmed" .)