You can click “Customize cards” in the bar to add more fields to the cards. You can also re-arrange the order of the fields on the card. The only field that must show on the card is the primary field.
If you want more linked records to show in a single linked record field, I’m afraid that you are out of luck. That cannot be customized and is mostly a matter of the length of the primary fields.
You could try adding a rollup field based off the linked record field and see if you can get more text in the preview that way (or at least a helpful …).