Saka is actually a short for "At saka", they're originally supposed to be together. And you're right it means "More over" or "And.... as well" .

“At saka” means “and also/moreover/in addition, etc.”. Oftentimes, with our normal speed of talking, when we say “at saka”, the sound of the first “a” is practically silent so what we say is more like “tsaka”. In fact, the “t” could hardly be heard and some of us at times don’t even pronounce it anymore. That may be the reason why you had the impression that you were only hearing “saka” without the “at” more often. “Si Mary, si Peter, at saka si Alice ang pumunta dito kanina.” = Mary, Peter, and also Alice, were the ones who came here earlier today. “Hindi na ako sasama sa inyo sa party kasi pagod na ako at saka kailangan kong gumising ng maaga bukas.” = I won’t go with you to the party anymore because I am already tired and moreover I need to wake up early tomorrow. There is also an idiomatic use of “at saka” when we add a “na” after it to mean, “at another time in the future”. Mary: Kailan tayo manonood ng sine? (When are we going to the movies?) John: At saka na. (Some other time.) At saka ko na gagawin yung pinagagawa mo. = I will do what you asked me to do at another time. Kumain ka muna at saka mo na ituloy ang ginagawa mo. = Eat first and then later, continue what you are doing.

Saka/Tsaka can also mean "and... too". Like "tsaka tubig" = "and water too" :)