Let's start from the beginning. There are four types of taxes:
1. Taxes on goods
2. Taxes on earnings
3. Taxes on assets (sale or purchase, or IHT)
4. Taxes on businesses (of which employers' NI is one)
All have their potential downsides, which would have to be overcome.
1. These are regressive taxes in general, hence my suggestion that they should be targeted, so that they hit the poorest least (or preferably not at all)
2. The problem is that those earning the most have the wherewithal to "protect" their earnings if taxes are too high, so rises can be self-defeating, hence my suggestion of an NHS surcharge on NI. Still I think things can be done with IT - e.g. raise the rate but increase the personal allowance, so that the poorest (who pay tax) are taken outside the tax system.
3. There are issues around people who are asset rich and cash poor. I can't think of any way around that, but honestly if people have to leave their 6 bedroom mansion in Surrey (and downsize to a 5-bed), because they got a £60k tax bill, then I'm not going to lose a lot of sleep over it. Again, I think this has to be aimed at the top end - the object is not to force Fred & Mabel out of their £200k semi.
4. The possible downside here is pushing firms out of business or (e.g. if you hit ERS NI) cause them to cut staff. Therefore the focus should be on the large companies who are not paying their fare share, i.e. changing the rules so that they can't avoid/evade paying a fair amount, based on their earnings in this country.