In the past couple weeks my students and I have been developing our vocabulary in regards to our busy schedules.

10 great words to use instead of “busy"

Informal term used to express an inflexible busy schedule.

Formal term used to express business, occupied is normally used with a time statement, quite popularly paired with + at the moment. 

Shows that you or the person speaking is busy right now but may have free time later.

Informal and communicates urgence of business. This term communicates that someone has their focus on multiple tasks and simply doesnt have room in their schedule.

Uncommon, formal
The tolerance level has reached a peak or ability/skills are at full capacity

Informal
Schedule is inflexible. and this communicates that you are doing more work or activities above your reasonable expectation.

Informal, common (Aus) 
A surprise business, like a flood is a surprise. Saying swamped communicates that you are busy but its surprising and unplanned.

Informal, common (UK and AUS) 
Expected, however creates imagery that you are drowning in your work or paperwork like how you would be drowning in snow if you were literally snowed under.

Formal, common 
The plate is a metaphor for someone's personal schedule. This term doesnt necessarily state the flexibility of the schedule though.

To have enough/rather a lot/too much on one’s plate at the moment

Informal, common, rude 
Synonym; has more important things to do

Can be rude as it kind of denounces another person's feeling of importance to a task/activity however in some situations it is not rude though.

Formal, uncommon 
The person has more important things to do during that time period, usually this is a response to someones enquiry. If you get told this, expect not to receive a valid response for a couple weeks.

To have other priorities today/this week /this month