Welcome!
Are you climbing RADS (aka "Yoyo")? The top device used above the Grigri for the foot loop is typically a hand ascender, though I guess other rope grabs could work too. Or, do you mean something different by backup?
One classic backup is knots in the rope below you, to limit any uncontrolled descent. The other is to stay low and go slow as you build confidence in your system.
Here's a good description of RADS with some good tips, just in case you haven't seen it:
https://www.newtribe.com/documents/tip4.htm
One thing that Tim points out in that article is that some climbers run a sling from their harness to the ascender to use as a safety, others don't. I started that way using the ascender as a backup, but ditched it pretty quick - it just didn't make sense.
Hanging out at height, I'll add redundancy with a lanyard or maybe a backup knot. On descent, I want firm control of the brake strand, and manipulating other devices gets in the way.
Other authors recommend leaving the ascender on for descent, and going a few feet at a time but I hated that even more.
Very few, if any, professionals on here climb with a Grigri. But regardless of what attachment system they use, the overwhelming trend is to know and trust that system without backup devices on the same rope. Ascenders as climbing aids, not life safety devices.
