No, EE Perk is not applicable in conjunction with any other offers. If your chosen plan is already discounted in any way (this will be confirmed when you add your plan to basket), then EE Perk cannot be used in conjunction with this plan.
If you choose to opt for an additional line product as an existing customer, the EE Perk discount code cannot be used. You would need to choose a full-priced product and apply your 20 per cent EE Perk discount code.