Does the Dense Ordering Principle imply the Order-Extension Principle? What about the converse?

Question

I have not been able to find any literature on this, so if somebody could point me in the right direction that would be useful. The Dense Ordering principle (DO) says that every set can be densely ordered, while the Order-Extension principle (OE) says that every partial order can be refined to a linear order. I was wondering if either of these statements is stronger than the other?

Answer 1

González, Carlos G., Dense orderings, partitions and weak forms of choice, Fundam. Math. 147, No. 1, 11-25 (1995). ZBL0821.03024.

There the author proves that the Prime Ideal Theorem does not imply that every set can be densely ordered. But since we know that it does imply that Order Extension principle, this means that DO is not a consequence of OE.

Conversely,

Pincus, David, The dense linear ordering principle, J. Symb. Log. 62, No. 2, 438-456 (1997). ZBL0890.03022.

Shows that the Kinna–Wagner principle implies every set can be densely ordered. On the other hand,

Felgner in

Felgner, Ulrich, Models of ZF-set theory, Lecture Notes in Mathematics. 223. Berlin-Heidelberg-New York: Springer-Verlag. VI, 173 p. DM 16.00 (1971). ZBL0269.02029.

Shows that Kinna–Wagner does not imply OE (p. 125), so in particular OE is not a consequence of DO.