Your question is too general, so a precise answer gets difficult to be set. First of all, you need appropriate account (able to store so much data). Does your account cover the capacity requirements? Next, since Dropbox is a sync service with a relatively conservative way of work, you have to take in mind that access point could be only on a single place (can't spread across mutiple volumes - partitions or drives). In this context you can't upload everything at once. You can use "Selective Sync" feature and upload the content step by step (folder by folder) and biggest step (content size) no more than available capacity of volume where Dropbox folder resides on.
Alternative could be instead moving content, Dropbox folder be moved and using the noted feature upload the content, drive by drive (could be expected easier - moving folders lower count). Don't forget to get Dropbox folder back to the initial place finally, otherwise data loss could be expected!
Probably many other ways could be described (or combinations of ways), but I hope the above gives the basic idea. The final solution will be of your choice, based on all details of your setup.