In some way or another, breaking up and staying friends is sort of like getting back together with an ex. Only this time you two will not have a romantic relationship. It will only be a platonic relationship. There are some benefits and drawbacks to this. Read further and then decide whether breaking up and staying friends is right for you.
In order to figure out if staying friends with your ex is worthwhile to you, you must figure out if either one of you still has strong feelings for each other. If either one of you still want to get back together romantically, then there can be no possibility of having a platonic relationship because there will always be some longing there to get really close.
One possibility of being able to stay friends is if you and your partner find partners of your own who satisfy your need for romantic and emotional love. At that point, you will likely have reached full closure and are now strong enough to have a friendship level relationship with your ex. One example of this scenario can be found on the Santa Claus movie with Tim Allen. His wife left him and found another man, while Tim found fulfillment somewhere else. They were both fulfilled, therefore they were comfortable being friends with each other, even though they were exes.
Another drawback of breaking up and staying friends is the very real possibility of one of you getting jealous once the other one begins to have a romantic relationship with another person. This is the downfall and most common reason of failed friendships between ex lovers. If one of you feels jealousy clamoring to the surface, then friendship after a relationship is not for you. More often than not, this scenario happens, and in order to prevent this, it is best to go cold turkey. Give yourself at least a couple of months before contacting them again.
Sometimes in order to feel the benefits of friendship, you do need to be apart for a couple of months. If this might sound awkward or counter intuitive, consider the fact that you don’t know what you have until you lose it. After a little time passes, you might realize what a friend you actually had. Or your partner might realize what a good friend you were and then come back to you with mended ways. Either way, a little time apart might do both of you some good.
The few benefits that do exist when staying friends after a breakup beg the question: Why? Why would you want to stay friends with your ex after a breakup? If your new romantic partner is okay with it, then that will be fine. But if they are not okay with it, then you will have to choose whether you want to continue the relationship with both them and your ex. Some people would view that as baggage while others would see it as something totally doable. It is entirely up to you.