My kitchen outlets are starting to wear out.
In many kitchens (In USA/Canada, anyway) kitchen outlets are wired as a MWBC with the two receptacles operating on different legs of the service. Rather than being at the same voltage, the hots on each half of the outlet are 240 volts apart (120 from neutral for each.)

If your "multi-outlet-adapter" internally wires the hots together (rather than feeding half of it's receptacles from one, and half from the other) it will presumably make a large nasty spark and hopefully trip the breaker when you plug it in.

Most adapters don't comment on how they are wired internally. Wiring the hots together would in general be a bad idea (as MWBCs to split outlets are not uncommon) and as such might be rare in well-designed products, but not all products are well-designed.

If you are replacing the outlets (receptacles) anyway, it might be worth replacing them with ones that don't need an adapter to give you more receptacles, or to add additional outlet boxes if you are finding the current outlets insufficient to your daily needs.