Once a test has started, it is not possible to edit the variants for that particular test. Note any other test settings that are not related to your variants are still editable. For example, if you run an image test, the images cannot be edited but if you’d like to include another child ASIN, then you can certainly do that.
That is because if you change anything in a variant, the results become meaningless immediately since it won't be possible to know for sure what caused the difference in sales, sessions and profits.
If you need to edit variants for a test that has started, you should pause/abort the test, then clone it, edit it and then you should be able to run it. The clone feature makes an exact copy of the current test - but you can still edit anything before you run it.