can I install 2024 turbortax premier and home and business on the same computer

No, and there is no need to do that.   Buying two versions of the desktop software for the same computer would just be a waste of money.   Every version of the desktop download can provide all of the forms and schedules to prepare personal tax returns.  You do not need two versions of desktop software.   They will not download/install to the same computer.   And if you were thinking that it would give you more than five federal e-files, it will not.   Five e-files is the IRS limit.

No, you cannot install more than one of the 2024 TurboTax desktop personal editions on the same computer.

The TurboTax desktop editions all include the same forms, schedules and worksheets.  You only get more help and guidance using the higher editions.  So, select which edition you want to install and then return the other edition for a refund.

Why do you need a second program on the same computer?  The Desktop program can prepare unlimited returns and efile 5 for free.  And you can use any version.  All the desktop programs have the same forms.  You just get more held in the higher versions.

But you can activate a second program.   Under Help - Switch Product - Activate new product. Don't know what that will do or what benefit you will get. Don't think it will allow you to efile more than 5.