When ownership is shared, you only indicate possession once:
We were invited to Linda and Carl's home.
The home belongs to both Carl and Linda. The same would be true for ownership that is not material:
Ira and Joe's idea went over well at the meeting.
This changes when ownership is separate. (Sounds a bit like we're talking law, doesn't it? Hang in there with me; it'll make sense.) In this case, each noun should show possession:
Only Freddy's and Lisa's offices were infested with bugs.
In this sentence, there are two offices. One belongs to Freddy and one belongs to Lisa. Clearly, they need an exterminator.
In this case, apostrophe choices aren't linked with singularity or plurality. Two people can share ownership of many items and the apostrophe is still used only once. Here, Fran and Liz own all the horses together:
At the farm, we rode Fran and Liz's horses.
Here, Fran and Liz own different horses:
At the farm, we rode Fran's and Liz's horses.
On a related note, it's sometimes difficult to figure out where to place an apostrophe when indicating possession with tricky words, such as compound or hyphenated words. In these instances, indicate possession only at the end of the word:
She stole her mother-in-law's purse.
We were appalled at the Post Office's advertising campaign.
The apostrophe is a little mark, but a mighty one. Use it with knowledge and confidence.