Bidding on more than one plot with an account is perfectly acceptable in the rules; doing so is a means of increasing your odds of winning a house in the lottery. However, you can only own 1 personal which means you can't accept a winning bid on both characters. Once notified that you've won, you'll need to decide which character will have the house. Because you didn't lose the bid on your second character you won't be able to get your full refund during the results period. Instead you'll need to wait until it ends and you default on your claim. Defaulting also includes a 50% fee so you only get half your gil back. That 50% fee is the risk you take in having multiple bids.

More detailed info can be found here.
https://na.finalfantasyxiv.com/lodes.../housing_land/