If you support anti corporatism, then you should support the abolition of private property.
No matter how much you want mom and pop shops to run the economy, market competitions, just like competitions in general, have a winner. Meaning a business eventually dominates the market share. If you want proof, then look up any industry and chances are that there were more companies in said industry in the 50s than today. This isn’t something that can be changed in neoliberalism, or even just capitalism in general, but is a default mechanism of it.
And before a liberal uses this as an argument, no, private property is not the same as personal property. Private property is capital or the means of production, such as factories, hotels, farms, etc… this doesn’t include your personal domicile, your own objects, or your land used for personal cultivation.
To summarize: Capitalism sux be a Marxist.