Speakers that sound like Grado headphones?

That is easy, none. Headphone listening gives a completely different balance and presentation than speakers, for example the room has no effect at all while with speakers it is the dominant factor. The two channels are totally separate unless you have a device to mix them while with speakers you always hear a mix. The headphones only have to move the small amount of air in your ear while the speakers have to drive the whole room.I have used Stax headphones to evaluate my system for 40 years now and I have yet to hear speakers, including electrostatics, which sound like them. You can try for a similar balance in the sound between the two, just don't expect too much.

I would echo that (pun intended). Speakers sound like speakers and headphones sound like headphones. I have Grados as well and they sound great with my vCan headphone amp. They don't sound like my speakers. Both fun and exciting, but different.

Which grado and what is your price range? What part of the sound do you like?

Most good brands (thiel,Wilson, B&W, Focal,dynaudio, etc) will out class your grados. Grados are bright and forward with little bass extention. But they are fast and dynamic.

Look for balanced speakers that lean toward the forward side (Thiel, Wilson Audio, small Focals 1027,1037) for a grado-ish sound. If you are tight on cash give Klipsch a go.

Brands that sound nothing like grados (and more like Sennhiezers) are Dynaudio, Sonus Faber, etc. They are neutral but lean toward the dark polite side.

Studio monitors in the near field.