Ask HN: Additional options awarded after vesting cliff – new cliff necessary?

I have worked at a startup a little over a year. My options package included the typical 1 year cliff, 4 year vest. I recently hit my one year vesting cliff. I am in the process of negotiating for more options. Assuming I am given more options, what does a typical vesting agreement look like in this case? Will I have a new set of options with a second vesting cliff one year from now, while the original set continues to vest at its predefined rate? Or can I negotiate rolling the new options into the same vesting package, so they vest at a constant rate and skip the cliff?