Can i add two different banks account - one for self assessment and the other limited company?

You've come to the right place for assistance, @finqwas-opkl35-g.

There are several banks that allow you to connect your personal and business accounts. You can search for your personal account, it might be included in our list. 

If you're unable to search your bank, I recommend contacting your bank to determine if personal account connections are available. The availability time frame depends on them. Make sure that you're also using the correct link or name when looking for it.

In case you're still unable to connect to your bank yet, you'll have the option to manually import your transactions. Also, you can request to have your personal account added to the list of supported connections. I'll show you how:

1. Open the Banking menu, then hit Add account.
2. Look for the exact bank's name, then scroll down until you see the Still can't find your bank? link. 
3. Enter the bank name and copy and paste the web address. 
4. Click on Request. 

Once done with connecting the account. you can start categorising and matching transactions.

Keep me updated by replying to this thread. I'm always ready to assist any additional concerns regarding banking or QuickBooks. Take the best care!