それに details

Examples

besides; and on top of that — piles a further supporting point onto the last one

この店みせ、安やすいよね。それに、店員てんいんさんも親切しんせつだし。

kono mise, yasui yo ne. soreni, ten'in-san mo shinsetsu da shi.

This place is cheap, right? And besides, the staff are nice too. casual

駅えきから歩あるいて五分ごふんです。それに、家賃やちんも相場そうばより安やすいです。

eki kara aruite gofun desu. soreni, yachin mo souba yori yasui desu.

It's a five-minute walk from the station. What's more, the rent is below the going rate. neutral

今日きょうは熱ねつがある。それに、外そとはひどい雨あめだ。出でかけるのはやめておこう。

kyou wa netsu ga aru. soreni, soto wa hidoi ame da. dekakeru no wa yamete okou.

I have a fever today. On top of that, it's pouring outside. I'll skip going out. neutral

し
し is clause-final, repeatable and flags the list as open-ended (安やすいし近ちかいし — more reasons implied); それに names one further point and claims nothing about what else could be said, which is why the two stack rather than compete — 安やすいし、それに近ちかい.
そして
そして only claims the next thing belongs with the last, so it will link two events in sequence (東京とうきょうに行いった。そして、大阪おおさかにも寄よった); それに adds a further GROUND pulling the same way as the last point, so it misfires on a bare sequence, and 安やすい。それに、まずい fails outright because the second point pulls the other way.
に加えて
に加くわえて hangs off a noun inside the sentence and skews written and businesslike (経験けいけんに加くわえて、語学力ごがくりょくも求もとめられる); それに is the ordinary spoken adder and needs only a clause boundary in front of it — 安やすいし、それに近ちかい is as good as a full stop.