We are planned to move our store to Magento 2.x and our current magento version is Magento 1.9.1.1 . Is all extensions used in our version will support on Magento 2.x extensions. We did core file modification also. Please advice us to upgrade 2.x is possible.
No all extension will not support Magento 2.x. If you bought extension from the extension vendor than ask them for the newer version of the Extension which you want for Magento 2.x. And for the core file you need to change it manually. And if you use theme then theme also not support to new version.
Basically I want to say you need to Migrate the data and extensions from the older Magento to Newer Magento. There is no any upgrade facility available in it.
Thanks and hope it will be understand.