Piggable plate heat exchanger assemblies enable piggable cleaning of interior surfaces thereof. Piggable plate heat exchanger assemblies include an inner plate member and first and second channel forming members with adjacently positioned first and second channel forming extension plates to enclose the inner plate member to form first and second channels for first and second fluid flow. Other piggable plate heat exchanger assemblies include plate members and first and second end members in conjunction with corresponding plate members positioned at first and second ends of corresponding plate members to form first and bypass channels to flow first and second fluids. Still other piggable plate heat exchangers include a plurality of plate members and a plurality of end members forming in conjunction with the plate members a first channel and a second channel in an interweaving relation for flow of a first fluid substantially normal to flow of a second fluid.