Can I use a second disk on my Time Machine as a backup for my MacBook Pro?

The other replies are true, if your MacBook Pro is old enough that it still has a user-replaceable optical drive, the optical drive can be replaced with a second hard drive. Not possible on Mac laptops made in the last few years where there is no optical drive, and the internal storage is not user-replaceable.

It is also true that a second internal drive is OK for use with Time Machine as long as it is not the only backup. A real backup has value only if it is separate from the computer; otherwise if something happens to the computer, the backup is also doomed, and then there is no backup.

However, what I will add to the discussion is that, whether you know it or not, in recent versions of macOS, Time Machine already maintains an invisible backup on the internal storage of your MacBook Pro. Time Machine maintains local "snapshots" which are a temporary local way to store backups when the actual Time Machine backup drive is not connected. If you have not connected your Time Machine backup drive in a while, your Mac probably has built up several Time Machine snapshots, and you can restore from them.

The next time you connect your Time Machine drive, the local backup snapshots are transferred to that, and the space on your Mac internal storage is freed up.

Sometimes the Time Machine local snapshots take up too much space on the Mac and can be manually pared down. You can do this in the Terminal, or using backup software that knows how to manage Time Machine snapshots like Carbon Copy Cloner.

If that is what you wanted to do with the second disk, put backups on an internal drive, then you don't have to do anything because macOS is already doing it with Local Snapshots.

I was not aware that you can put a second disk inside the MacBook Pro. Unless you are replacing an internal DVD drive with a second SSD?

If you can somehow install a second disk, you can use it for the backup drive with Time Machine. But that is not recommended because if your Mac has a major failure and cannot start up, you won't be able to access the backup drive. Or a power surge or physical damage to the computer could render both the primary drive and its backup drive inoperative. Or if the computer is stolen you lose your backup also.

Much better is to use an external drive for the backup.

In rare cases of fairly old MBP, you could, as D. I. Johnson, said install a second drive inside your mac.

This is not possible in any mac since about 2013, with one exception (a 13" model that was still for sale for some time after).

But even if you can, it is not a great idea.

If your mac is lost or stolen, there goes your backup as well. If your mac has some accident, odds are the backup drive goes as well.

It is ok if you use that as part of a multiple backup strategy, like if you have an additional backup that is stored separately.

OWC Data Doubler, for example: https://eshop.macsales.com/item/OWC/DDAMBS0GB/?gclid=EAIaIQobChMI3oqG0MLu8gIVWW5vBB08vggxEAAYASAAEgIWh_D_BwE