The Cherries may be all but safe from relegation under coach Andoni Iraola so far.
However, Tavernier insists that 41 points with seven games to go is not the sum total of what they want to achieve.
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Asked about pushing for a European spot by BBC Radio Solent, Tavernier replied: Mathematically it's an option, but our goal is to achieve that club record for points.
That's what we're aiming for. And then if we get that, we're over the moon, but we just keep climbing each week, we have to keep fighting, taking it game by game."