  We consider NS-NS superstring model with several ``magnetic'' parameters
$b_s$ (s=1, ...,N) associated with twists mixing a compact $S^1$ direction with
angles in $N$ spatial 2-planes of flat 10-dimensional space. It generalizes the
Kaluza-Klein Melvin model which has single parameter $b$. The corresponding
U-dual background is a R-R type IIA solution describing an orthogonal
intersection of $N$ flux 7-branes. Like the Melvin model, the NS-NS string
model with $N$ continuous parameters is explicitly solvable; we present its
perturbative spectrum and torus partition function explicitly for the N=2 case.
For generic $b_s$ (above some critical values) there are tachyons in the $S^1$
winding sector. A remarkable feature of this model is that while in the Melvin
N=1 case all supersymmetry is broken, a fraction of it may be preserved for $N
>1$ by making a special choice of the parameters $b_s$. Such solvable NS-NS
models may be viewed as continuous-parameter analogs of non-compact orbifold
models. They and their U-dual R-R fluxbrane counterparts may have some
``phenomenological'' applications. In particular, in N=3 case one finds a
special 1/4 supersymmetric R-R 3-brane background. Putting Dp-branes in flat
twisted NS-NS backgrounds leads to world-volume gauge theories with reduced
amount of supersymmetry. We also discuss possible ways of evolution of unstable
backgrounds towards stable ones.
