My 8 yr. old calico, Sandy, has been doing her bm right outside the litter box on and off for about a month now. I am puzzled by her behavior because she is a very clean cat. She also vomits her food often right after eating it. We also have another cat and I am wondering if she is eating too fast to be sure that she gets enough food. The other cat is somewhat of a glutton and will go from her dish to Sandy's. I am most concerned about her missing the litter box like she is. She urinates in the box like she should.
Going outside the litter box does not mean Sandy is not a clean cat. She most likely doesn't know quite what she is doing or why.
It sounds like you are pretty perceptive about her behavior. Cats frequently regurgitate due to their imagined or real competition with another cat for the food. They eat too fast and ...well you know the rest.
This same "competition" can be responsible for eliminating outside the box. She may be frustrated about the other cat and food and without knowing it, is taking out her frustration by going outside the box.
She also may not like defecating where she urinates. That is not unusual
She also may feel threatened in some way by the other cat or other objects or noises near the litter box.
She could also have a medical problem that has developed such as constipation or soft stool or other discomfort when she defecates. Cats can acquire a litter box aversion when they have experienced discomfort or fear while they were in the box.
I would suggest you do something to help her feel like she will always have enough food such as feed them separately or at least have two bowls of food in two different rooms.
Also, if you don't know already, watch to see if she eats faster and vomits more when she is eating dry food or canned food. If you are only feeding one type, try the opposite. If you are feeding one brand, try something different with a different protein source. (If the present food is mainly poultry, try beef, etc.)
It also is a good idea to always have at least one more litter box than the number of cats you have. The boxes should be in different locations. They also should not have lids or liners.
If the above suggestions do not solve the problem, a visit to the vet for an exam and possible bloodwork is in order. Take a fecal sample along.
Good luck. These problems can almost always be worked out with persistence and patience. Thank you for writing,