The trouble is, every one is different. Some mothers may be able to mixed-feed without losing their supply altogether. Others might not even be able to do what you've done already without finding that bf is finished for them.
Another alternative for you is to see a qualified Breastfeeding Counsellor from one of the voluntary organisations (NCT, Breastfeeding Network, La Leche League etc) who might find out why dd is still feeding so frequently at 4 months. Could be she is not correctly attached to the breast, or brought off too soon, or falls asleep before completing the feed. The services of a bf counsellor are free and confidential, and leave you under no obligation.
Also you might consider expressing some milk, either by hand or by using a breastpump, and offer that to your dd after she has breastfed.
Personally, I found it useful to be able to feed lying down for night feeds. If you don't already do that, a bf counsellor can help with the technique.
You are bound to be tired, caring for a 4 month baby and there are other things you can do to combat it, eg have a rest during the day, maybe when dd has a nap or when some one else takes her out in the pram. The number of men I see wheeling children around here esp on a Sunday morning!