Double Goldbach plus epsilon conjecture

Let $n$ be a positive even integer. A pair of Goldbach representations consists of primes $q_1,q_2,q_4,q_5$ satisfying

$$q_4<q_1\leqslant q_2<q_5<n$$

and

$$q_1+q_2=q_4+q_5=n.$$

There is also a prime $q_3$ with $q_5<q_3<n$. Double Goldbach plus $\varepsilon$ conjecture. Every positive even integer $n$ admits primes $q_1,q_2,q_3,q_4,q_5$ such that

$$q_4<q_1\leqslant q_2<q_5<q_3<n$$

and

$$q_1+q_2=q_4+q_5=n.$$

This strengthens Goldbach-type assertions by requiring two ordered representations of the same even integer together with an additional intervening prime; the source provides no resolution.