Shamir's scheme for implementing an $(n, k)$ sharing of a secret $S$ involves a random polynomial $F$ of degree $k-1$ such that $F (0) = S$. Each of the $n$ shares of $S$ is a pair $(x, F (x))$ for $x$ between $1$ and $n$. Consider a setting with $n$ participants $P_1, P_2, \dots, P_n$, and 2 secrets $S1$, $S2$. Each participant $P_i$ is given a distinct share $S1_i$ of secret $S1$ based on a suitable polynomial $F1$ for an $(n, t)$ sharing and a distinct share $S2_i$ for secret $S2$ based on a suitable polynomial $F2$ for an $(n, t)$ sharing. Show how a new principal $A$ can communicate with existing participants to learn $S1 + S2$, without learning either $S1$ or $S2$.
You can use the fact that Shamir secret sharing is linear. Each participant $P_i$ adds their two shares locally $S1_i+S2_i$, then sends this value to $A$.
Because of the linearity of Shamir secret sharing, this will allow $A$ to reconstruct to get $S1+S2$. Furthermore, none of the participants learns the sum (not a stated requirement in your question, but presumably something that you are looking).