The BJT characteristic curve
You are correct in your assumption that to vary Vce you must adjust the resistor values. The equation for the collector current (Ic) is as follows:



Now solve for Vce and you get:



Plug in Ic = Beta*Ib:



We know that beta and base current are generally constant (in your question), so as long as Vcc is also constant the only variable that you can adjust is the resistance.