Let p be a prime and K be a p-adic local field. We study the stack of quasi-de Rham $(\varphi,\Gamma_K)$-modules, i.e. $(\varphi,\Gamma_K)$-modules that are de Rham up to twist by characters. These objects are used to construct and then study the so called the paraboline varieties, which parametrize successive extensions of quasi-de Rham $(\varphi,\Gamma_K)$-modules of a certain type. On the automorphic side, We construct relative eigenvarieties, and prove the existence of some local-global compatible morphism between them via showing the density of ”classical points”.