Yes.    Any  person,  including  a  believer,   can  have   an  evil  spirit   in their   body   and/or    their   soul,  which   is  the  mind,  emotions  &   will of   a    person.     However,   the    "spirit"   of    every   human   being    is reserved    exclusively   for   God    to   come   into   &   dwell   in.

Jesus   said,    "that   which  is   born  of  the  Spirit   is  (human)   spirit.."  (John 3:6)   showing  that   when   a    person   is   born  again   [John 3:7] it   is   the   person's   own   "spirit"   that   is   birthed   by  God's   Spirit.

But,  even  a  Spirit-filled  believer  can  still  have  enemy  spirits  that  are  influencing   &   even   attached   to   their   body    [like  cancer  or  some other   physical   afflliction]      or     influencing   or    attached    to    their mind,   emotions   or   will,    hindering   advancement   in   Christ.

Importantly,   the    Greek    word    in    the    New   Testament    for    our English     translation    of      "demon-possessed"      has     the     actual definition    as    being     "demonized".      So,   whether   a   person   has an    evil  mindset    or    is   completely   taken   over  by   demons    who control     that    person's     "will"      (Mark 5:1) ,     then   according   to Scripture    that    person    is     "demonized". 

Scripturally,   there   are   definitely  various   levels  of   demons   &   also various  levels  of   being   'demonized'   ranging  from   a   person  being oppressed   with   evil   spiritual   activity   to   the   most   extreme  case  where   the  person  is  completely  taken  over   by   demons  which   I call     'full-blown'    demon-possession,     as    in    the   case   of    the demoniac  found  in   the   Gospel   of   Mark  Chapter 5.         [ Rob Conrad ]
demon  possession

Can even a believer have demons?
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