Yes, it is possible, and generally preferred. The filter is linear and obeys superposition: as long as the attenuation is sufficient for the total amount of ripple, you are set.
Mind that this does nothing about common mode noise, which depends critically on layout, and cable length. You may also want other tweaks, such as dampening (an R+C or electrolytic somewhere; C36 already present is promising, though the EEE-HA1J470UP doesn't specify ESR and looks like it may be pretty high), TVS (to clamp inrush overshoot or other transients), polarity protection, or etc., depending on the application.
Note that the local bypasses can also be at least partially shared; how much, depends on the distance between ICs, and whether they are synchronized. Probably, if more than a few cm apart, the full set of capacitors should be provided for each IC; if adjacent, use, say, two 0.47us and two 4u7s each (i.e. add one and one).
As long as I'm mentioning capacitors by value, note that 0.47u doesn't do much here: you get the same ESL from any value of same chip size capacitor. I would use all 4u7s and be done with it; besides, staggered values tend to invite more problems than they solve.
If synchronization is an option, forcing out-of-phase or interleaved operation minimizes input ripple, and a single set of capacitors will suffice for both (again, assuming the ICs are adjacent). Maybe even less, but it's safe to assume given as a minimum (reducing parts count would be more of a production optimization option, I'd say).
I should point out that both buck converters operate at the same switching frequency.
are they sync'd? \$\endgroup\$