Nao, I meet such a wording mostly in books.
It translates as 'all the more'. Now, how it works:
Part I
"[something] тем интересней, что [a fact]"
"....было тем интересней, что"
"...казалось ему тем интересней, что..."
"...казалось ему тем более интересным, что..."
"интересней" = "более интерес[...]". Two ways to form a comparative.
By [...] I mean the ending needed (short/full, f/m/n, sg/pl, case).
It all means: [smthng] is/seemed interesting. But [the fact] makes it Even More interesting.
"Тем" = Inst. of "то", 'that'.
"То" refers to [the fact]. Instrumental case because... it one of archaic meanings of Instr.: [the fact] MAKES it 'more interesting', DUE TO [the fact] it gets more interesting.
"Это обещало прибыль тем бОльшую, что..."
For "большАя" only one comparative form exists: бОльшая.
*более большАя - ????:-/
Here 'even more' refers to 'favourable':
"Казался перспективой тем более благоприятной..."
An inversion is possible (a bit archaic):
"Казался перспективой благоприятной тЕм более, что..." (тЕм is stressed sometimes to distiguish from the next one).
Here another comparative gets impossible. You can't put 'благоприятней' into here.