summing a column based on either of two conditions being met

[squallleonhart]

I have a spreadsheet that has columns for total claims by subscriber and the % of overall claims the subscriber has for the group they are part of. I would like to sum up the total claims column based on either of two conditions being met. If the total claims are greater than a certain threshold or the % of claims the subscriber is responsible for is more than a certain percentage. These two events are not necessarily mutually exclusive so I can't just create two sumifs and sum the results. I could sum each event and then subtract when both criteria are met, but that seems inefficient.

Is there any way to do this in one formula?