How do you know two dogs will be friends?

Long story short, my 10-year-old Corgi was recently diagnosed with a brain tumor and is scheduled to be put down on Thursday. Thanks in advance for any condolences.

Prior to this decision, we were deciding on whether or not to get our other dog, Browser, a companion. Callie, the Corgi, and Browser have never been friends. They've never been enemies, but they don't really play together. Browser spent the summer with my partner's family, being best playmates with one of their dogs and I can definitely tell she misses her buddy.

We're going to the shelter this weekend, like we had intended before scheduling Callie's appointment, and there are a few dogs there that have caught our attention. Our plan is to meet the dogs on Friday, and then bring Browser back to meet the dogs we liked on Saturday.

But, my experience with matching up two shelters dogs is limited. Is there a way to tell that they'll be friends/playmates, as opposed to just tolerating each other (which I already know how to determine)?

Thanks in advance for any advice.

For the record, the dogs we've chosen to meet are a Cairn Terrir mix, a Bichon Frise/Poodle Mix, and two Daschund/Terrier mixes, all of them at least 2 years old and all of them heartworm positive (which we already decided we are more than willing to take on and treat).

And is it a good idea to do two meetings, one with Browser and one without? My partner thinks maybe if we see the dog a second time, they'll remember us and be a little calmer?

Personally, I know I'm going to fall in love with one of these dogs and won't want to leave them in the shelter another second.