Trying to make consumption taxes more progressive is not impossible but it is uphill battle since any consumption tax is inherently regressive since lower income people spend larger share of their income on consumption than higher income people (see discussion of this in Blanchard et al. Macroeconomics: A European Perspective).
Probably the most straightforward way how consumption tax can be made more progressive is to tax goods consumed more frequently by upper income people at higher rate than the goods consumed by lower income people.
While this is doable in a sense that it is technically possible to implement, it is often not very economically efficient for various reason. Here are some of them:
Luxury items tend to have higher price elasticity than necessities. One of the most basic rule of taxation is the famous 'Ramsey rule' that suggests that inelastic goods should be taxed more than elastic goods (see Stiglitz Economics of the Public Sector). Hence, such attempt to make consumption tax more progressive goes against the most basic rule of optimal taxation.
Consumption does not carry information about your type (in terms of income) perfectly. Low income people might buy luxuries even if they do that much less often than high income people, and there are high income people who might distaste luxury consumption (e.g. consider Bill Gates who famously dresses modestly) and thus while doing this can make the tax more progressive it is to a degree tax on a lifestyle rather than a fully being more progressive tax. For example, in the Netherlands where I live food for bunnies and guinea pigs was for long time taxed with different VAT (presumably because government determined that rich people prefer bunnies (bunny food had higher VAT), completely ignoring they are in fact perfect substitutes).
Research shows that if government has access to both consumption and non-linear income taxes (i.e. government levies them at the same time), it is always more efficient, even with Ralwsian social preferences (the most redistributive preferences there are), to have flat consumption tax and highly progressive income tax. This is because income actually caries information about your type. Thus if you care about having progressive tax system, and you consider tax system as whole not just separately, and you want to achieve maximum progressiveness, it is better to do that all through income tax rather than trying to change VAT (see Atkinson and Stiglitz 1980. Lectures on Public Economics or Jacobs Principles of Public Finance).
In fact, from economic perspective there is little difference between income and consumption since all income is eventually spent on consumption. Saving is just postponed consumption (although saving can have beneficial effect on growth). However, income carries with itself information that can be more effectively used for redistribution than consumption that carriers very little information usable for redistributional purposes. Consequently, if your goal is maximum progressiveness of tax system you would optimally achieve that all through income tax, and the only reason why you would not set consumption taxes to zero is to alleviate some distortions that income taxes cause on labor market (As a matter of fact in the special case when utility function is weakly
separable between commodities, and labor the consumption taxes would be fully redundant - this is known in public econ as the Atkinson-Stiglitz Theorem). Using progressive consumption tax is only optimal in situations where you forbid government from using progressive (non-linear) income taxes or income taxes altogether (or perhaps there might be some special cases - but full review of literature on this issue is beyond scope of SE answer).
There are some other proposals such as the X-tax you mentioned. However, note X-tax is not a pure consumption tax. X-tax has both consumption and income component as X-tax also combines consumption tax with taxes on wages and so on (see Bradford, 2008). Consequently, I do not believe these proposals would qualify for what you are looking for in the question since you ask conditionally on "if consumption taxes were used more than income tax".
Next, you could also make consumption tax progressive by applying consumption tax at a flat rate first and afterwards let people with low incomes claim tax rebates on their consumption. This is probably the most efficient way how to make consumption tax more progressive (even though most of the previously mentioned caveats still apply). This tax can be designed in various different ways, you can read more about it in for example Seidman (2013) or Seidman: The USA Tax A Progressive Consumption Tax. However, once again you can't get away with involving those 'pesky' incomes in the tax system design. Again this is because incomes carry most information relevant to progressive taxation, but in this case I think it would satisfy conditions imposed in your question since even though this consumption tax is based on income (since low income people get rebates), it does not necessarily involve directly levying income taxes (such as X-tax, which includes extra taxes on labor earnings).