high level monsters varies ....
it used to be 1 to three (jinzo, airknight, a spellcancellor or a horus or on rare occasions, even a phoenix)
But today's yugioh deck has more choices to special summon a tribute monster quitte easily
Thank you treeborn frog,
thatnk you giant germs and other floaters
thank you d-heros
thank you advanced ritual art
and now it is not unheard to have up to eight tribute monsters...( jinzo, and multiple copies of Mobius, Zaborg, Thestalos, and Razer the wind monarch, as well as an airknight, or Two or Three!!
generally it isnt the amount of tribute monsters, its if your hand is keeps getting unbalanced hands or not
for example having only monarchs on the first turn, only to be hit with confiscation and all u have is one brain control..
or drawing three giant germs and a premature and a call of the haunted,
anyway the point is the more tributes u have, (say five in your case) you would need x number of cards to guarantee you can bring him out from your hand...in your case at least ten ... (call o haunted, premature, treeborn, brain controls, soul exchange, cyber dragon or other special summon creature, ancient rules, instant fusion, etc)
any of these cards will help to balance your deck!!!