This work introduces general multisection identities expressed equivalently in terms of infinite double products and/or infinite double series, reordered by way of their indices. From this reordering, we derive new product and summation identities involving special functions including gamma, hyperbolic trigonometric, polygamma, and zeta functions. It is shown that a parametrized version of the multisection identity exists, a specialization of which coincides with the standard multisection identity.