There's an obstruction to embedding $n$-complexes in $\mathbb R^{2n}$ provided $n \geq 3$ due to Shapiro. 

MR0089410 (19,671a)
Shapiro, Arnold
Obstructions to the imbedding of a complex in a euclidean space. I. The first obstruction.
Ann. of Math. (2) 66 (1957), 256–269. 

Could you be more precise on how you want to modify the your complexes that originally are in $\mathbb R^3$, your special case?