Good question; these pairs of words can be quite similar. "Beyond that, ..." feels more formal than "Besides, ...". "Beyond that ..." might be used in writing or in making a point of argumentation rather than simply listing points or listing reasons, like "besides". "Besides" is more common. "To acknowledge" is neutral, i.e., it can be used for something good or bad. You can acknowledge a gift from a neighbor; you can acknowledge that you were late for a meeting. "To admit" is used when you did something wrong, and are finally (reluctantly) saying so. You might admit that you didn't tell an acquaintance that you were really at home when you said you would not be.

Beyond is further away. Besides is closer My dog is currently beside me. I can’t see the cat though as it’s gone beyond my garden Admit means to confess. Acknowledge is to accept something (as fact) or to greet The criminal admitted his guilt. I acknowledged the advice my Dad gave me to treat others nicely

Beyond mean ......separate from him....and besides mean with things....good luck