How to deal with high peaks traffic campaign on Twitter?


we are developing a platform that generate personalized video and post back them on Twitter.
Of course, we follow the rule for automated post on twitter … but we still have a problem on dealing with high peaks.
In fact, our campaign are usually very short (a couple of day) where people are invited to engage posting a tweet with specific hashtags or retweet or (more often) interact with a conversational advertise.

When a person is engaged by the campaign’s hashtags, we generate a video for him/her and we send a tweet reply with the video attached.

From past experience, we have been told that we can only post a maximum of 60 posts per hour in case the posts have a video attached even if the account has been elevated and it has been agreed a more heavier traffic.

So, I’m wondering if there is some king of arrangement to allow us to send more that 60 posts per hour to deal with high peaks. In some campaigns, we would have post about 300 videos per hour.

Is there any way to request an increase of such limit… even if it would include pay Twitter for doing so ?