I am a holder of an equity savings account and also a book-entry account for investing in corporate stocks. In addition, I own shares in investment funds. Will this cause a punitive tax increase for me?

No, as long as you hold just one equity savings account, it is no problem. The punitive increase would be imposed if you had more than one such account. However, in the case of ordinary book-entry accounts, there are no restrictions on how many accounts you can open. You can also participate in many different funds at the same time freely; and it does not even matter if the funds are in different banks.