Consider that the bitwise OR operation is cumulative and non-decreasing. The maximum OR will be achieved when the shifted element contributes as many new set bits as possible to the final result.

For each element in the array, calculate the potential OR if that element were shifted by `2^k`. This involves OR-ing the shifted element with all other elements (or their prefix/suffix ORs) to determine the maximum possible contribution.

Optimize the calculation by precomputing prefix OR (OR of all elements before index `i`) and suffix OR (OR of all elements after index `i`). Then, for each index `i`, compute the OR of `prefix[i-1] | (nums[i] << k) | suffix[i+1]` and track the maximum value across all indices.