on top of that
Used to add together things of similarly charged natures, either positive or negative. I won the lottery and I realized I can fly! My mother passed away, and I got stuck in the raptor cage again.
and then, accordingly
Used in situations where a first action/condition results in/provides a base or justification for a subsequent action/condition. Hard, right? It's like: This is a very serious conversation about abstinence education の上で, you shouldn't laugh out loud. Or: I confirmed that it was, in fact, 100% Colombian Pure 上で、I authorized the buy.
(My book defines this as "以上は" which you may recognize as grammar point 3)
and then, what will possibly happen;
and then, what should happen;
and then, what I would like to happen
After a condition or action, used to express the speaker's strong feelings about what comes next, whether it be a judgment, a hope, or a guess. When you adopt a child 上は、you're supposed to feed it EVERY day.
Yosh! This one we learned for 3kyuu. Freebie.
during the interval
While one condition continues to be the case, something else gets done. You'll hear the following example A LOT if you dine with Japanese people.
My favorite thing to say when people accuse me of traveling too much: 日本にいるうちに。。。
(Same as above with a negative form introduced)
Before one condition begins, something else gets done.