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There is no Taming Effectiveness multiplier to change. You can change either the Taming Speed or the Food Drain multipliers to make sure dinos eat fewer times before they are fully tamed (and thereby maintain higher TE %). By increasing the Taming speed, dinos will require fewer feedings to Tame, thereby boosting TE. By lowering food drain, dinos will eat less often and give you higher TE and bonus levels. The two values are relative, so if you raise or lower both an equal amount, TE will be just as hard to achieve as vanilla rates, but taming will take longer or be quicker depending on whether you raised or lowered Taming Speed. When Taming Speed is higher relative to Food drain, higher final TE will easier to achieve. The quality (and suitability for each species) of the food used means less effectiveness is lost per feeding.
How many levels your dinos will gain is also based on their wild level. The formula is effectively L × TE / 2 (rounded down), where L is the wild dino's level and TE is the Taming Effectiveness you have when taming is complete. So for a level 10 dino and 85% Taming Effectiveness, it will be 10 X 0.85 / 2 = 4.25 (rounded down to) 4 bonus levels.
Since you don't mention what the wild dino's levels or final TE was, it's hard to guess if what you're seeing is normal or not, but the maximum amount of bonus levels possible is roughly 50% of the dino's wild level (Level 150 and 99.9% TE results in 74 bonus levels).