I have a 256 ssd drive on my Mac book pro and an external 512 ssd drive. Can I make them look like one drive?

If the computer is running, awake or asleep, and the drive is disconnected the data will almost certainly be lost. If the computer is turned off it won't know about the disconnection and reconnection....probably. It just isn't worth the risk.

What you are doing is too risky to consider. Instead why not use an external SSD and clone the hard drive to it. Install the research software on the external and when you are working on research boot from the external. Otherwise boot from the internal.

It appears you have settled on a solution (combining drives) to some problem/goal you have in mind. "Because" is not an answer we can work with. You are asking for a reason. You want to accomplish something by combining drives. Tell us what it is you are trying to accomplish and we will try to help you reach that goal. Combining drives for no reason is of no value.

It is possible to create a Fusion drive with an internal and external drive - go online and search for "how to make a fusion drive". Then ignore it unless you use the notebook totally as a desk computer. If at any time your external drive were disconnected from the computer the Fusion drive would be kaput and you'd be saying bye bye to your data. And if you do decide to go ahead be super super compulsive about backing up.

Wrong "reply to" ... sorry.

CarbonCopyClone is software that can be an incremental backup of a drive. It also knows how to clone an active (not just idle) drive to a larger drive while using the full size of the target by expanding the partition. bombich.com, $39. You may want to have a coupe of alternate ways of creating "one button" clones of your critical research data.

My opinion.

If terrence270 tries to use the home made Fusion drive a TimeMachine backup will be vital and since I'm a belt and suspenders kinda guy I'd use CCC as well. I love having a clone. Among other reasons, if my drive dies I can get back to work immediately after rebooting. With just TimeMachine I'll have to wait for the backup to restore.

If he decides to run the entire computer from an external (I'm actually doing that with a mini that has a rotational drive) he won't notice much of a speed difference at all. (I should have mentioned this in my original reply.) A second external for backing up is highly suggested. Fact is, at home I use two TimeMachine external drives and one clone external. One TM backup is always at work so one TM drive gets 1 week behind but is away from the house. I use a similar system at work.

Why?