Oh, I see. The complete sentence is: My father had finally agreed to buy a pet dog for me with a few conditions of course. You can state it this way: My father had finally agreed to buy a pet dog for me under a few conditions, of course. However, it's not wrong to say: My father had finally agreed to buy a pet dog for me on a few conditions, of course. But, it sounds slightly strange to say: My father had finally agreed to buy a pet dog for me with a few conditions, of course.

Hi Elizabeth ^_^ i rather say I agree to some condition that ..... I agree with some of your conditions I agree on some of your conditions ...... both are correct .............................................. agree (with someone) (about / on something | agree (with something) to have the same opinion as sb; to say that you have the same opinion: example: He agreed with them about the need for change. I agree with her analysis of the situation .......................................................... be agreed (on / about something ) | be agreed (that … ) if people are agreed or something is agreed, everyone has the same opinion about something example: Are we all agreed on this?