Individually divisible?

I have chosen four integers a,b,c,{\color{#D61F06}a}, {\color{#3D99F6}b}, {\color{#20A900}c}, and d{\color{#69047E}d} so that all five of the following sums are values divisible by 3:

  • a+b+c{\color{#D61F06}a}+{\color{#3D99F6}b}+{\color{#20A900}c}
  • a+b+d{\color{#D61F06}a}+{\color{#3D99F6}b}+{\color{#69047E}d}
  • a+c+d{\color{#D61F06}a}+{\color{#20A900}c}+{\color{#69047E}d}
  • b+c+d{\color{#3D99F6}b}+{\color{#20A900}c}+{\color{#69047E}d}
  • a+0+0.{\color{#D61F06}a} + {\color{#333333}0}+{\color{#333333}0}.

Are b,{\color{#3D99F6}b}, c,{\color{#20A900}c}, and d{\color{#69047E}d} also guaranteed to be divisible by 3?

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