Synonyms for Busy (same or very similar meaning)
WordNet sense 1 (keep busy with):
occupy
WordNet sense 2 (overcrowded or cluttered with detail):
fussy
WordNet sense 3 (not plain; decorative or ornamented):
fancy
WordNet sense 4 ((of facilities such as telephones or lavatories) unavailable for use by anyone else or indicating unavailability; (`engaged' is a British term for a busy telephone line)):
in use
WordNet sense 5 (held or filled or in use):
occupied
WordNet sense 6 (intrusive in a meddling or offensive manner):
meddlesome, officious, interfering, busybodied, meddling
WordNet sense 7 (tending to intrude (especially upon privacy)):
intrusive
WordNet sense 8 (having ones attention or mind or energy engaged):
engaged
WordNet sense 9 (full of activity or engaged in continuous activity):
active
From the ODE community, based on WordNet
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