This will be dependent on a variety of circumstances.  I think that one can envision how a classroom that features higher leveled thinking can be constructed.  In my mind, I think that a classroom that spends a great deal of time on higher ordered thinking has to be one that features a great deal of resource material for students to access.  Higher ordered thinking can be seen in how students can be free to pursue different approaches to content, which is why there would be enough resource material in the form of learning centers or classroom libraries in order to appeal to student curiosity and love of learning.  At the same time, I think that the physical structure of the classroom would be one where students are able to move with ease, as higher ordered thinking tasks might involve physical configurations that are not always standard.  Additionally, I think there would be an emphasis on differentiated instruction as the teacher that embraces higher ordered thought is willing to scaffold instruction in manners that allow students to pursue different paths to the the same content end of comprehension.

How much higher level thinking can one include when planning and teaching lessons?

I am not certain that there is a "limit" to the amount of higher ordered thinking that one can feature in the design and execution of lessons.  I think that much of this depends on several variables that will determine how much higher ordered thought is featured in lesson design.  The first is the overall comfort of the teacher.  I believe that the best higher ordered tiered instruction and learning happens when the teacher is comfortable with the material and comfortable with being able to perch out on the branch where there is much in way of student inquiry and exploration.  Teachers need to develop comfort with this and understand that it might be acceptable to develop tasks and assignments where students generate the thought and products that reflected higher ordered thinking.  Additionally, teachers have to engage in enough instruction with the rudimentary elements so that students can have some frame of reference with which to place these ideas into a higher ordered context.  It does not help students to approach higher ordered thinking tasks if they lack the basic instruction.  Students cannot progress with higher ordered tasks on fractions and number theory if they lack understanding on what a fraction is and how it is represented.  It is here where teachers must focus their attention, setting up lower level thinking skills in higher ordered contexts.