Take (somebody) on board?!

No - it does NOT mean to take someone onto a ship/boat/plane etc etc!!!
to take someone on board means 'to hire them as part of the team or company'.
'I think she wants to keep me on board' means 'She wants to keep you as part of her team/employee of her company/her group.'

on board字面上的意思是在船上,在火車上,or在飛機上(要視乎上文下理)
但其實指的是用車輛or飛機旅行 (to be traveling on some vehicle)

所以,"take (sb) on board"的意思就是"帶著某人乘坐汽車(or飛機)去旅行"

但"I think she wants to keep me on board."的意思就應該偏向是"我認為她想把我留在車上(or飛機上)"

不知哪一個可以幫到你呢?或者你再告訴我吧

Take (somebody) on board?!

採取(某人) 在船上?!