Fascinating question about grouting

[RattusRattus]

I have just moved into a new house and have noticed that the grouting in between the floor tiles in the kitchen, utility and hallway is really shallow so it's incredibly hard to clean. Either it's impossible to get the mop to reach the dirt down there or dirty water pools and dries in it when you wash the floor. It's a very large area so it's not really an option to scrub it out with a grouting cleaning brush every week (it would literally take me a day to do it all).

It is possible to re-grout on top of dried grout? Someone said to me that the new grout wouldn't stick to the original grout. If it won't stick what are my options?

There are good arguments for and against removing the old grout. No doubt removing the old grout is better, but can you get away with adding new grout on top?

It seems to me that the best way it to remove the old grout to a depth of at least 4mm (there is a special tool that does this). If you already have a depth of 4mm, you should be able to add grout over the old.

Be sure that the old grout, or the remains of it, is absolutely clean and dust-free.