No, according to the EAT in Country Weddings v Crossman. The employment tribunal can do nothing other than to make an order for joint (or joint and several) liability, as the case may be.
If there is an issue between the parties who have been found liable as to the relative share of the liability that they should bear, this is a matter that has to be determined in the County Court or the High Court under the provisions of the Civil Liability (Contribution) Act 1978.
This was a TUPE case in which the employment tribunal had chosen to apportion the compensation for a breach of the regulations so as to make the whole sum payable by the transferee. The EAT held that it was quite clear that the TUPE regulations provided for the liability to be joint and several between transferor and transferee and that this was in line with the general principle laid down by the Court of Appeal in London Borough of Hackney v Sivanandan & Ors where orders for compensation are made by employment tribunals in claims involving liability of more than one party.