One reform they would like is open trade. The UK is well placed to trade with developing countries, but the high tariff (and non-tariff) external barriers that we sign up to as EU members make this nigh-impossible. Also, the CBI wants the single market to be completed. At present there is a single market in most goods (though often it is very much harder to export to other EU countries than it should be under the rules). But we are still waiting for a single market in financial services, in which the UK has a particular strength.
Will the CBI get the reforms they want? Unlikely. There are just too many vested interests wanting to prevent the UK's financial sector from getting in to their markets. And if the EU were to drop its barriers against foreign trade, why would anyone want to remain an EU member? They could quit and still get the free trade benefits. The EU would have no members left, except the ones living on its subsidies.
People dream of other scenarios. A Norway solution where, as an EFTA member, it enjoys access to the EU market. The downside is that it also pays a contribution to the EU despite getting no say over how its rules are made. But then the UK gets no say in how its export markets in the US, China and elsewhere set their rules either. The Switzerland arrangement has been mooted. It has negotiated scores of bilateral trade deals with the EU. But it is a very complicated set of arrangements. Another model is Turkey, part of a customs union with the EU. But again, it faces non-tariff barriers and has no say in things.
Sadly the EU cannot grant any such arrangement to anyone – otherwise the whole membership, led by the UK, would be queuing up to demand the same concessions. So I remain skeptical that the EU can be reformed in any meaningful way. Of course, if you believe it has a mission in promoting ever-closer political and cultural union, it still has a purpose. But economically, it can only stick together if it keeps its trade barriers high. That is not good for the EU, nor the world.