さらに details

Examples

furthermore; and beyond that — adds the next item or stage on top of what was just stated

一次いちじ審査しんさでは書類しょるいを確認かくにんします。さらに、二次にじ審査しんさで面接めんせつを行おこないます。

ichiji shinsa de wa shorui o kakunin shimasu. sarani, niji shinsa de mensetsu o okonaimasu.

The first round is a document check. Beyond that, there is an interview in the second round. neutral

台風たいふうで電車でんしゃが止とまった。さらに、幹線道路かんせんどうろまで通行止つうこうどめになった。

taifuu de densha ga tomatta. sarani, kansen douro made tsuukoudome ni natta.

The trains stopped because of the typhoon. On top of that, even the main roads were closed. neutral

本ほんサービスは無料むりょうでご利用りよういただけます。さらに、会員かいいんの方かたには割引わりびきクーポンを差さし上あげております。

hon saabisu wa muryou de go riyou itadakemasu. sarani, kaiin no kata ni wa waribiki kuupon o sashiagete orimasu.

This service is free to use. In addition, members receive a discount coupon. formal

それに
それに is the everyday spoken adder and will tack on an afterthought of any size; さらに measures its addition as a further step along the same line, so it fills reports, procedures and announcements — dropping さらに into a chat about a cheap restaurant sounds like reading from a brochure.
に加えて
に加くわえて hangs off a NOUN inside the sentence (経験けいけんに加くわえて語学力ごがくりょくも), so what it adds must be nameable in one phrase; さらに stands before a whole clause and adds an entire event or stage.
しかも
さらに counts the next step in a series and belongs to written and formal-spoken register; しかも carries the speaker's own verdict that the extra fact is remarkable, and it is at home in conversation — which is why a procedure list takes さらに and a complaint or a sales pitch takes しかも.

もう一度
Both come out as "more" — もう＋a quantity measures out one further helping and is at home in requests and plans (もう一杯いっぱい, もう少すこし); さらに before a quantity counts the increment against what has already accumulated rather than against the here and now (さらに二割にわり増ふえた), and it is the written one, which is why a price that has risen twice is reported with さらに.