At the outside
Definition 1 of 2
Pro Tip 1/3Worst-Case Estimate
Used to indicate the longest time or largest amount something might possibly take or need. 
If traffic is bad, I’ll be there in 30 minutes, at the outside.
Pro Tip 2/3Limit Expectations
Helps set limits to prevent over-expectation on durations or quantities. 
We can save up to $200 on our budget, at the outside.
Pro Tip 3/3Context Sensitive
The meaning is clearer within specific contexts, especially involving time or money. 
The conference will last two days, three at the outside.