それとも details
Examples
or — offers a further alternative, normally the last one, and asks the listener to choose
コーヒーにする?それとも、紅茶がいい?
koohii ni suru? soretomo, koucha ga ii?
Shall we make it coffee? Or would you rather have tea? casual
打ち合わせは今日でしたっけ。それとも、明日でしたっけ。
uchiawase wa kyou deshita kke. soretomo, ashita deshita kke.
Was the meeting today? Or was it tomorrow? neutral
会場でお受け取りになりますか。それとも、ご自宅までお送りいたしましょうか。
kaijou de o uketori ni narimasu ka. soretomo, go jitaku made o okuri itashimashou ka.
Would you like to collect it at the venue? Or shall we send it to your home? formal
Formation
それとも、clauseattaches to plain clause
Notes
proposal instead (コーヒーを入れるよ。それとも、紅茶がいい?).
A flat declarative list of options takes または or もしくは.
Related patterns
Similar
か is the question particle inside each alternative and joins them only by juxtaposition (コーヒーにしますか、紅茶にしますか); それとも is the conjunction BETWEEN them, which is what lets the second alternative start a new sentence after a full stop, or be added as an afterthought once the first has landed.
Lookalikes
One と apart and constantly mistyped for each other, but それとも needs what follows it to be interrogative and asks the listener to pick, while それも asks nothing and merely adds a detail to a statement already made.