[TETRAMETHYLAMMONIUM HYDROXIDE][3] *Journal of the Chemical Society* 87 (1905): 955-961: 


>Practically the preparation of tetramethylammonium hydroxide
fiom its salts resolves itself into a question of solubility as follows.
In general, the equation  

>$$\ce{NMe4X + MOH = NMe4OH + MX}$$

>will represent a real action proceeding nearly to completion if N, X,
and the solvent are so chosen that all the substances except MX shall
be soluble, or at least that MX shall be much less soluble than either
of the original reacting substances. This principle was applied by
Hofmann in his preparations with water as solvent. For M and X
he chose either the pair Ag,I or Ba,SO4, in both of which cases MX is
practically insoluble in water.  

>It is clear that if the general application of the above principle is
justifiable, tetramethylammonium hydroxide may be prepared from a
tetramethylammonium salt by means of potassium hydroxide if we
so choose X and the solvent that of the substances represented
in the equation

>$$\ce{NMe4X + KOH = NMe4OH + KX}$$

>all shall be soluble except KX.  

...  

>An estimation of the strength of the base by means of the velocity
of saponification of methyl acetate in N/80 solution showed that it was
somewhat weaker than sodium hydroxide. The velocity constants obtained at 25 [degrees] were 0.0106 and 0.0115 respectively, so that if the
strength of sodium hydroxide is represented as 100, that of tetramethylammonium
hydroxide, under the above conditions, will be represented by 92.  

So by two independent methods it is shown that TAMH is much stronger than pKb=4.2.  Firstly, the halide cannot not be converted to the hydroxide by adding metal hydroxide, unless an insoluble halide is produced to force the equilibrium forward.  Seconding, it is shown by velocity of saponification to be only slightly weaker then NaOH.   


  


  [1]: http://jes.ecsdl.org/content/142/2/621.full.pdf+html
  [2]: https://books.google.com/books?id=Gb9RAAAAMAAJ&q=%22tetramethylammonium%20hydroxide%22%20complete%20dissociation&dq=%22tetramethylammonium%20hydroxide%22%20complete%20dissociation&hl=en&sa=X&ved=0ahUKEwjb9rnMnPLZAhVNyGMKHUjvCO8Q6AEISDAI
  [3]: http://pubs.rsc.org/-/content/articlepdf/1905/ct/ct9058700955