If your staff are so overworked they are having emotional breakdowns but you can't afford to hire any more staff then it would appear your business model is failing. i.e you're not making enough money from the product or services you provide, and/or you are paying your staff too much, and/or you are putting far too much emphasis on non core business activities which do not produce revenue.
If you don't do something to fix this fast you risk having people go off on long term sick leave due to stress. Alternatively, as Cottoneyes suggested, you will lose staff, which will only exacerbate the situation, or both!
So some suggestions;
- Remove or minimise expectations of non core business activities
- Increase the cost of your products or services and employ more people (immediately)
- Eliminate any obvious inefficiencies is your work processes.
Just one other thing, profit - are you trying to make too much profit? is that why there is no budget for additional staff?