Who is the manufacturer of the new larger hard drive? On their websites, both Seagate and WD make available for free download customized versions of Acronis True Image software that is made for exactly this job - cloning an older drive to a new larger drive. The restriction is that WD's version will only make the clone TO a new drive from WD, and Seagates' will only work TO a Seagate (or Maxtor) HDD.
Simply copying old drive to new never seems to work - there are entirely too many hidden files that don't get copied. A good cloning utility is definitely the way to go. It also makes the processes of Partitioning and Formatting easy as part of the cloning process.
You don't say how your "few OS's" are structured. They may all be in one Partition that takes up the entire old disk's space. More likely you have the old disk split up into Partitions with one OS per piece.
For situations with one Partition on the old drive, when you use the Acronis software to migrate you have control over the amount of the new drive to use in the Primary Partition it creates. Many will choose to use ALL of the new disk's space in one Partition and make it Bootable, just like the old structure but with much more space. Also check that, with a big new drive, the File System it installs is NTFS (unless you know there's a reason to restrict yourself to FAT32). Just make sure to read the options so that it does make your Primary Partition the size you want, and not some default other size.
In the case of multiple partitions on the old drive, you get three choices. The simple one is just to duplicate all the old partitions, and leave a whole bunch of Unallocated Space on the new drive in which you can later make more Extended Partitions. The next is what's called Proportional Partitions: Partitions on the new drive collectively take up all the drive, but each is increased in size so that they all are in the same proportions as on the old drive. The third option is that you manually set each Partition on the new drive to a size you choose.
I have not done this with a multi-Partition drive containing several OS's, many of which (presumably) are Bootable Partitions. So I am not sure how you specify that several Partitions on the new drive are Bootable, but I'm sure there is a way. Check the software's menus and documentation.