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Are there any other types of consciousness (viññāṇa) in Theravada outside the six sense media consciousnesses?
According to Theravada perspective, there are only six types of consciousness (which you've already mentioned). This is a categorization of consciousness based on its sense base. Every consciousness falls into one of these six. In Abhidhamma, there are many categorizations [based on wholesomeness, sphere of the being (kāma-loka, rūpa-loka, arūpa-loka), worldliness, etc...] can be seen of same consciousness which mentioned in Suttanta desana.
In Abhidhamma,
What about rebirth linking consciousness? Is that a type of consciousness outside the six sense media?
No, it falls under mind consciousness and we can say it also falls under resultant consciousness more precisely according to Abhidhamma.
There are 10 consciousness (*) arise in eye, ear, nose, tongue, and body sense bases (2 consciousness in each with the division of wholesome resultant and unwholesome resultant). All the other consciousness arise in mind base.
Note 1: (*) :-
Hence,
Note 2:
Note: This is what I understood. I may be wrong but not Dhamma.
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Both, Abhidhamma and Suttanta traditions, trying to follow the Buddha, are informed about 7 kinds of "knowing", while the 7th does not relay on a (of the six) sensual surface, does not grasp after being touch.
Bhante Thanissaro elaborated well on the topic "consciousness without surface".
Consciousness without feature,
without end,
luminous all around:
Here water, earth, fire, & wind have no footing.
Here long & short
coarse & fine
fair & foul
name & form
are, without remnant,
brought to an end.
of (the activity of) consciousness,
each is here brought to an end.
— DN 11