I have this cobble stone flooring

From: http://homeguides.sfgate.com/regrout-top-grout-34870.html

How to Regrout on Top of Grout

Over time, grout can become dirty, grungy, cracked and missing in places. Regrouting is a task that almost any homeowner can accomplish. Time and patience to remove some of the old grout to allow clean grout to bond to the surface is the key to doing a job that makes your tiled bathroom look like new. You don't need to remove all the grout, or even most of it, but removing the dirty grout on the surface gives the new grout something to which to bond. After all, grout primarily is just cement.

1 Don a face mask. Scrape out some of the old grout with a grout saw, which is available at any home store. Removing much of the grout isn’t necessary; just get it down enough from the surface to allow new grout to bond.

2 Vacuum up any loose dust and particles. Thoroughly wash the wall to remove grout dust and any other film.

3 Mix grout according to package directions. Spread the grout using the grout float, forcing grout into all joints and pulling the excess off with the edge of the float like a squeegee. Wash grout off the surface of the tile with a damp sponge while smoothing the joints at the same time. Allow the grout to dry to a haze, then again wash it with clean water. Allow the grout to dry, then buff it with a clean dry towel. Allow the grout to dry for one week.

4 Spread grout sealer onto new grout joints with a dry clean cloth. Allow the sealer to soak into the joints, then wipe off the surface of the tile.

5 Caulk corners and any areas between tile and another surface. Cut the tip of the caulk tube to a size equivalent to the joint. Using steady pressure on the caulk gun, push the tip of the tube across the joint, leaving a smooth, consistent joint. Smooth any rough places with a wet finger.

Things You Will Need

• Face mask
• Grout saw
• Vacuum
• Sponge
• Grout
• Grout float
• Clean cloth
• Grout sealer
• Caulk
• Caulk gun
• Utility knife or scissors

Tips

• Grout saws have a serrated, carbide-tipped blade that gets through the old grout with a minimum of effort.
• There are grout saw attachments for power tools available that make the removal part of the job easier. Extra care must be taken, however, to prevent chipping and cracking the tiles.

Warning

If there is mold or mildew, make sure it is completely removed before regrouting. If not, the problem will reoccur. Use a bleach solution to clean and eliminate mold and mildew in joints after using the grout saw.

That's the rustic style! Yes, you can re-grout, but you would have to remove all of the grout, otherwise any you just filled in with would crack and come out - look awful and be a danger.......

I'm not a mason, but I would regrout it, but put the slabs closer together. The picture that you show, it looks like the slabs themselves are uneven. This is something to ponder. Good Luck!

I would rent an industrial floor machine that scrubs and picks the dirty water back up like a carpet machine first. If it comes clean apply grout sealer in a squeeze bottle such as a ketchup bottle. That will help keep it clean for years.

How to get the stink out of garbage disposals

Every so often I throw some citrus peel in it (lemon will do, too) & flip the switch. Smells marvelous! There is also a product called "Plink" that is sold in grocery stores. That works pretty good, too. But the peel is more fun & cleans the blades, too.