Secret sharing scheme with ability to add or update share number
With Shamir's Secret Sharing you can add as many shares as you want, as long as the threshold and the secret is unchanged. 

You can see that neither the generation of the polynomial that produces the shares nor the reconstruction of the secret by polynomial interpolation require the parameter $N$ (number of shares), but only the threshold $k$. 

Of course the number of shares $N$ should obey $N\leq p-1,$ since they need to be obtained as polynomial values at distinct points of the field $F_p$ and one point, usually zero, is reserved for the secret. You can increase $p$ if needed, but shares need to then be recomputed modulo the new prime you choose.