@Matthew Powell, (I'm also not an attorney or CPA) but I can tell you my recent experience with this. I have several properties that were purchased under my name to get the good financing that an LLC can't. I also have a Texas Series LLC that allows me to add additional series LLCs by simply filing a new assumed name in Texas. As long as I follow the Texas property code and keep all the books separate as @Costin I. mentions, the code should provide protection for those new LLCs. This saves the cost of filing a new LLC (only cost is $30 for assumed name filing fee), but I had fees to transfer title of my property to the LLC since I purchased it under my name (mostly lawyer fees since the county has no online service).
One thing that caused a bit of back-and-forth was that when I told the insurance company to change the named insured on the policy to the series LLC, they didn't keep my name on it. When the bank caught wind of this, they sent me a kind letter saying that the insurance policy and the loan did not match and I need to fix that. Concerned that the bank would execute the dreaded DOS (due-on-sale) clause, I called them and told them what I was doing (full disclosure). Despite the clear DOS clause on my loan, they said as long as my name was somewhere on the policy, they would be okay. I kept the named insured of the policy with my series LLC (advised by my attorney), but added my name as an additional insured (along with the bank for the loan). I got another letter from the bank after that, but when I called they said it was a mistake and all was good with the policy and title (again despite the DOS clause).
Note that my loan DOS clause says I have 30 days to remedy the issue before they can actually call the loan. If the bank wants to call the loan after that, it will cost them and take time, both of which they don't want to spend. So I didn't see the risk unacceptable to change the name on the title (could always change it back to prevent the loan call or work something out with the bank).
Note that this is a bit of buyer beware. Theoretically, I should have protection since I have the title under the LLC and the named insured is the LLC. However, I understand that when it comes down to a law suit, plaintiff attorneys may still try to go after you personally even if it is under the LLC. It surely helps to deter the attempt (kinda like a burglar alarm deterring a burglar, but the really good ones will by-pass it if the prize is worth it), but no guarantees and who knows what will happen in court. Even so, this is still a good option to mitigate personal protection risk in real estate.
You may want to consider a series LLC under one of the States that does them. The state codes currently have some differences, but there is work on legislation that would unify the code across the country. If passed, it should provide us much better protection since it should have more standing in the courts.