Transform an almost positive definite matrix to positive definite matrix.

Question

Matrix A (n by n) is constructed as followed.

1. $A(i,i)= -\sum^{k=n}_{k=1}A(i,k), k \neq i. $
2. A is symmetric.
3. All the off-diagonal elements are negative except two elements $A(p,q)$ and $A(q, p)$: $A(i,j)<0$, when $i\neq j, i,j \neq p, i,j \neq q.$

Therefore the matrix is diagonal dominant for all the rows except row $p$. $A$ is almost a M-matrix. Is there any technique we can transfer this matrix $A$ to a positive definite matrix? Actually transforming part of $A$ to positive definite will be good enough.