Given the success (to a certain extent) of Commander Data to create another android, mainly his daughter Lal, did not that encourage starfleet research to attempt to make use of his partial success and attempt their own creation? Seeing what went wrong and maybe create more androids and getting a little bit closer to Dr. Noonian Soong work?
In the official Star Trek TNG Universe, no further work was done by Data on his daughter Lal's malfunction, most likely due to his schedule as a Starfleet Officer and his eventual death in Nemesis. Since Lal was created in 2366 and Data dies in 2379, a considerable amount of time has passed since her cascade failure. If such technology existed, it would make sense Data would have been the first recipient of such technology.
He did attempt to perfect the emotion technology but suffered a cascade failure in a similar fashion. Her body was likely taken to the Daystrom Institute where Starfleet scientists were likely able to work directly with the technology.
We are never told if they were ever successful at replicating the Soong's work. What we do know is if Data was able to create a Soong-type android using the scientific technology onboard the Enterprise, this would probably spur Starfleet Research to try even harder using the results of Lal as a guideline.
Memory Alpha's Apocrypha for Lal indicates:
In the short story "The Embrace of Cold Architects" by David R. George III (collected in the Star Trek: Myriad Universes anthology Shattered Light), Lal's creation was delayed after Data missed a vital scientific conference until the return of the Borg, allowing Picard to 'distract' the Borg by focusing on Lal and the long-term implications of her existence after he became Locutus of Borg, allowing Riker timeto give the order to destroy his Borg cube and kill Locutus before the Borg could find and adapt to their attack. Lal's subsequent breakdown was then averted by the intervention of Doctor Noonien Soong when he 'summoned' Data to him, Soong's expertise allowing him to repair the damage to Lal's neural net. With the information of how to create stable androids, the Federation began creation of a new race of android soldiers intended to fight the Borg, but Data is able to destroy their prototypes.
In the novel Cold Equations: The Persistence of Memory, it is revealed that Lal's remains are kept at the Daystrom Institute, along with the remains of her 'uncles'; Soong's three original prototypes, B-4, and Lore. She is briefly stolen by the Breen, but is recovered thanks to the Enterprise-E and Doctor Soong- still alive after transferring his mind into an android body-, who subsequently manages to restore Data. Data then resolves to find the mysterious immortal known as Flint- based on reports that Flint was responsible for reactivating Juliana Tainer after her positronic net shut down, hoping that Flint will be able to help him restore his daughter.