Double the relative amount of oxygen and carbon dioxide in the atmosphere.
Presumably, this still falls within the realm of "Earth-like".
As already noted, entire populations of humans have already adapted to live at ~15,000 feet, and trees grow up 10,000+ ft where atmospheric pressure is about 69.6 kPa. The altitude you want is 25,000 ft, which has an average pressure of 37.6 kPa.
Let's focus on the altitude trees thrive at: 10,000 ft.
The problem with high-altitude life, as everybody else has mentioned, is that the air density is too low to support life; the air density at 37.6 kPa is too low for large organisms to live. In particular, the problem isn't low air density overall. Humans need enough oxygen and plants need enough carbon dioxide to live, so it's the density of these two gases we care about. So if you can alter the composition of the atmosphere a little bit, you can achieve the same density of these two gases on Earth at higher altitudes on your Earth-like planet, while still keeping atmospheric density about the same.
Using a little ideal gas law, for any gas in a mixture, when we try to achieve the same density at two different pressures, we get:
$$
\chi_2 = \chi_1\frac{P_{T1}}{P_{T2}}
$$
where $\chi_1$ and $P_{T1}$ are the molar ratio and total pressure at the higher pressure, and $\chi_2$ and $P_{T2}$ are the molar ratio and total pressure at the lower pressure, respectively.
The molar ratio of the three gasses of interest in Earth's atmosphere are ~78% nitrogen, 21% oxygen, and .03% carbon dioxide.
When we stuff the numbers into this equation, we get a new atmosphere which is about 61% nitrogen, 39% oxygen, and 0.06% carbon dioxide, and the atmospheric pressure at 25,000 ft is still the same as Earth: 37.6 kPa.
This calculation assumes that the temperature is the same at both altitudes, but we would of course expect a lower temperature at higher altitudes. If we drop that assumption, the equation becomes:
$$
\chi_2 = \chi_1\frac{P_{T1}T_2}{P_{T2}T_1}
$$
which means decreasing the temperature at the higher altitude actually makes it easier to achieve our desired oxygen and carbon dioxide densities, so you don't actually need to double the amounts of these gases.
Dealing with the cold
Incidentally, the first equation above also enforces the same temperature at both altitudes, so doubling both gases will also keep the temperature at 25,000 ft on your Earth-like planet the same as 10,000 ft on Earth.
You can also use the second equation to play with the temperature at your higher altitude to achieve some desired combination of temperature at 25,000 ft and sea-level conditions. Sea-level conditions follow from your new relative amount of oxygen and carbon dioxide. (See side effects below.)
Resulting ecology
The primary factor we've changed is the altitude range that large mammals and plants can survive and thrive at. This means the ecosystem should be similar to those seen in mountainous environments near 10,000 ft on Earth.
An important caveat here is that land life evolved from ocean life, and there's obviously a large distance between oceans and 10,000+ ft mountain ranges. Thus, whatever early amphibious life evolved would need to deal with much higher oxygen levels at sea level.
Side effects
Just as the temperature on your new planet is equal to the temperature on Earth at a lower altitude, this means the sea-level conditions of your planet will also be some combination of higher pressure and hotter than on Earth. This is because increasing the relative amount of oxygen and carbon dioxide will make the atmosphere more dense, overall.
This means the oceans will necessarily be hotter, as well. The effects of this can be complicated, but it would be easier for life to emerge due to greater energy abundance.
The planet as a whole is almost identical to Earth
The above approach doesn't change the mass or size of the planet, so it's gravity remains the same.
Average sea level is almost completely unrelated to atmosphere composition, so you can have the same land and ocean topography.
