(defvar project--next-dd nil)

(defun project--with-next-dd (fun &rest args)
  (advice-remove 'command-execute #'project--with-next-dd)
  (let ((default-directory project--next-dd))
    (apply fun args)))

(defun project-switch-project (dir)
  (interactive (list (funcall project-prompter)))
  (setq project--next-dd dir)
  (advice-add 'command-execute :around #'project--with-next-dd))