Fitting Three-Dimensional Data with Parameters

Question

I have been trying to fit a model of rate equations to data of three dimensions. The rate equations in my model are as follows.

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x2'[t] == k1 (1 - (x2[t] + x3[t] + x4[t])) - k1*x2[t] - k5*x2[t] + k5*x3[t]- 2*k2*x2[t]^2 - k3*x2[t]*x3[t] + k3*x3[t]*x4[t], 
x3'[t] ==  -k5*x3[t] + k5*x2[t] + 2*k2*x2[t]^2 - 2*k4*x3[t]^2, 
x4'[t] == k3*x2[t]*x3[t] - k3*x3[t]*x4[t] + 2*k4*x3[t]^2,

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I am trying to fit to data with the five parameters k1,k2,k3,k4,k5. The data itself is composed of 100 points with three coordinates per point. I have attempted to fit the model by applying the following code.

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equation1 = {x2'[t] == 
    k1 (1 - (x2[t] + x3[t] + x4[t])) - k1*x2[t] - k5*x2[t] + 
     k5*x3[t] - 2*k2*x2[t]^2 - k3*x2[t]*x3[t] + k3*x3[t]*x4[t], 
   x3'[t] ==  -k5*x3[t] + k5*x2[t] + 2*k2*x2[t]^2 - 2*k4*x3[t]^2, 
   x4'[t] == k3*x2[t]*x3[t] - k3*x3[t]*x4[t] + 2*k4*x3[t]^2, 
   x2[0] == 0, x3[0] == 0, x4[0] == 0};

sol = ParametricNDSolve[
   equation1, {x2, x3, x4}, {t, 0, 10}, {k1, k2, k3, k4, k5}];

fit = FindFit[datax234, 
  x4[k1, k2, k3, k4, k5][t] /. sol, {k1, k2, k3, k4, k5}, t]

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The above returns an error which results because of unequal number of variables. How can I fit to data of three dimensions this way?

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EDIT: Some data as requested. The three columns represent x2, x3, and x4. Each row is a three coordinate point made by the corresponding values.

0   0   0
0   0   0
0   0   0
0   0   0
0   0   0
0   0   0
0.001137656 0   0
0.001137656 0   0
0.001137656 0   0
0.004550626 0   0
0.007963595 0   0
0.007963595 0   0
0.009101251 0   0
0.009101251 0   0
0.012514221 0   0.001137656
0.011376564 0   0
0.018202503 0   0
0.023890785 0   0
0.035267349 0   0
0.04778157  0   0
0.058020478 0.001137656 0
0.064846416 0.004550626 0
0.084186576 0.003412969 0
0.101251422 0.006825939 0
0.122866894 0.004550626 0.001137656
0.149032992 0.010238908 0.003412969
0.164960182 0.011376564 0.004550626
0.188850967 0.022753129 0.003412969
0.218430034 0.026166098 0.004550626
0.246871445 0.034129693 0.007963595
0.251422071 0.040955631 0.010238908
0.266211604 0.045506257 0.011376564
0.278725825 0.053469852 0.017064846
0.283276451 0.062571104 0.020477816
0.301478953 0.070534699 0.023890785
0.313993174 0.089874858 0.023890785
0.317406143 0.100113766 0.027303754
0.348122867 0.109215017 0.038680319
0.349260523 0.119453925 0.039817975
0.34698521  0.135381115 0.056882821
0.352673493 0.14334471  0.050056883
0.372013652 0.151308305 0.060295791
0.374288965 0.153583618 0.062571104
0.340159272 0.167235495 0.070534699
0.376564278 0.177474403 0.085324232
0.377701934 0.179749716 0.087599545
0.389078498 0.194539249 0.088737201
0.386803185 0.202502844 0.089874858
0.37883959  0.202502844 0.081911263
0.386803185 0.204778157 0.09556314
0.377701934 0.219567691 0.104664391
0.377701934 0.226393629 0.105802048
0.395904437 0.215017065 0.118316268
0.393629124 0.22298066  0.122866894
0.391353811 0.220705347 0.125142207
0.377701934 0.219567691 0.136518771
0.364050057 0.216154721 0.154721274
0.353811149 0.236632537 0.146757679
0.359499431 0.215017065 0.158134243
0.333333333 0.22298066  0.170648464
0.323094425 0.224118316 0.187713311
0.33105802  0.224118316 0.177474403
0.328782708 0.23890785  0.195676906
0.324232082 0.227531286 0.221843003
0.308304892 0.228668942 0.233219568
0.295790671 0.236632537 0.240045506
0.296928328 0.236632537 0.229806598
0.287827076 0.250284414 0.228668942
0.299203641 0.246871445 0.229806598
0.300341297 0.245733788 0.224118316
0.30261661  0.252559727 0.230944255
0.290102389 0.252559727 0.240045506
0.300341297 0.25483504  0.248009101
0.304891923 0.259385666 0.237770193
0.304891923 0.242320819 0.258248009
0.299203641 0.259385666 0.260523322
0.287827076 0.253697383 0.274175199
0.268486917 0.266211604 0.269624573
0.275312856 0.255972696 0.279863481
0.276450512 0.265073948 0.283276451
0.282138794 0.237770193 0.285551763
0.279863481 0.232081911 0.30261661
0   0   0
0.274175199 0.258248009 0.290102389
0.288964733 0.261660978 0.273037543
0.276450512 0.257110353 0.299203641
0.268486917 0.244596132 0.291240046
0   0   0
0   0   0
0   0   0
0   0   0
0   0   0
0.248009101 0.23890785  0.33105802
0.22298066  0.234357224 0.358361775
0.22298066  0.23890785  0.342434585
0.217292378 0.244596132 0.353811149
0.22298066  0.240045506 0.359499431
0   0   0
0.208191126 0.246871445 0.3629124
0.205915813 0.257110353 0.370875995
0.210466439 0.229806598 0.353811149