Nope that is not possible. If you add the “correct” php.ini handler for your particular server then that is what the server will be directed to use. BPS does not do anything else with handling php/php.ini files. This is a static setting that you add to your .htaccess file with static htaccess code. The php/php.ini handler is either correct for your server or it is incorrect. There are no other factors involved in this equation.
Note: Since a php.ini file is a server configuration file then you need to kill/restart your web services or reboot your server any time you make server configuration changes so that those new changes/settings will be “seen/loaded” on the server.
Also the host server may or may not allow you to change some server configuration settings. In other words, if your server does not allow you to change a particular setting then the server will ignore whatever setting you use in a php.ini file. Only your host would be able to tell you whether they allow or do not allow you to change something on your/their server.