Part of Object Goes Through Plane When Falls

As with all simulations, make sure you use realistic properties for your objects - ie, each domino should be a realisic 'real world' dimension with suitable real-world mass and centre of gravity. If need be, set your Scene to suitable units so that your objects do not have to be unreasonably scaled (eg, if working with very large objects set the scale to Kilometres, if very tiny, maybe set to Milimetres or Micrometres, etc.).

Ensure you have 'Applied Scale' to all of your objects. This helps with producing a consistent simulation.

In Scene Rigid Body World parameters consider increasing the Steps Per Second and/or Solver Iterations above the default values (defaults are 60 and 10) - eg, 6000 and 600 would not be unreasonable and shouldn't slow down the simulation too much. Avoid excessively high values as this can result in rounding discrepancies which can affect the stability and accuracy of the simulation. If in doubt, change one value by a factor of, say, 10 and re-try the simulation to see if it makes it better or worse before deciding on whether to change it back and/or change something else. Note that there are no 'universal best values' for these - it depends on your situation and simulation requirements.

If you're still getting intersections, consider enabling the Collision Margin in the Physics properties Rigid Body settings. This defaults of 'off' and can be enabled and a margin set. The default (0.04m - 4 cm) will likely be way too large (depending on your scene units and what it is you're simulating) - try the lowest permitted value first (0.001m (1mm)) and try higher values if still getting collision issues.

Using these changes I managed to get a clean simulation without clipping. If you still cannot get the expected results, please edit your question to add further details.