I'm pretty sure this has a simple solution and thought I would take advantage of the expertise here. I want to get rid of the base group of zero for "treat" in the following probit estimation so that I can then use the margins command to obtain the discrete change in the probability when treat goes from zero to one with the the variables set at the given values. In other cases I have succeeded but this more complicated case confounds me. I know there must be an easy way to force the redundant terms to stay out of the estimation, and then the margins command (I think) will come back with the desired estimate. All variables are binary except for z1, which is essentially continuous. I don't want to have to re-specify the model and choose different base groups.

Code:
. probit ybin i.treat#c.e4#c.d2014 i.treat#c.e4#c.d2015 i.treat#c.e5#c.d2015 i.treat#c.e4#c.d2014#c.z1_dm4 i.treat#c.e4#c.d2015#c.z1_dm4 i.t
> reat#c.e5#c.d2015#c.z1_dm5 d2014 d2015 e4 e5 c.z1 c.d2014#c.z1 c.d2015#c.z1 c.e4#c.z1 c.e5#c.z1, vce(cluster id)

note: 0.treat#c.e4#c.d2014 omitted because of collinearity
note: 0.treat#c.e4#c.d2015 omitted because of collinearity
note: 0.treat#c.e5#c.d2015 omitted because of collinearity
note: 0.treat#c.e4#c.d2014#c.z1_dm4 omitted because of collinearity
note: 0.treat#c.e4#c.d2015#c.z1_dm4 omitted because of collinearity
note: 0.treat#c.e5#c.d2015#c.z1_dm5 omitted because of collinearity
Iteration 0:   log pseudolikelihood = -1319.6071  
Iteration 1:   log pseudolikelihood =  -1289.157  
Iteration 2:   log pseudolikelihood = -1288.9143  
Iteration 3:   log pseudolikelihood = -1288.9143  

Probit regression                               Number of obs     =      2,180
                                                Wald chi2(15)     =      41.82
                                                Prob > chi2       =     0.0002
Log pseudolikelihood = -1288.9143               Pseudo R2         =     0.0233

                                                  (Std. Err. adjusted for 545 clusters in id)
---------------------------------------------------------------------------------------------
                            |               Robust
                       ybin |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
         treat#c.e4#c.d2014 |
                         0  |          0  (omitted)
                         1  |   .2874317    .088649     3.24   0.001     .1136827    .4611806
                            |
         treat#c.e4#c.d2015 |
                         0  |          0  (omitted)
                         1  |   .1536865   .0717827     2.14   0.032     .0129949     .294378
                            |
         treat#c.e5#c.d2015 |
                         0  |          0  (omitted)
                         1  |   .0197738   .0831368     0.24   0.812    -.1431713    .1827189
                            |
treat#c.e4#c.d2014#c.z1_dm4 |
                         0  |          0  (omitted)
                         1  |  -.0021974   .0592601    -0.04   0.970     -.118345    .1139503
                            |
treat#c.e4#c.d2015#c.z1_dm4 |
                         0  |          0  (omitted)
                         1  |  -.0301018   .0462808    -0.65   0.515    -.1208105    .0606069
                            |
treat#c.e5#c.d2015#c.z1_dm5 |
                         0  |          0  (omitted)
                         1  |   .1291999   .0789543     1.64   0.102    -.0255476    .2839474
                            |
                      d2014 |  -.2243262   .2136812    -1.05   0.294    -.6431336    .1944812
                      d2015 |  -.2271168   .2476411    -0.92   0.359    -.7124844    .2582508
                         e4 |  -1.939124   1.258554    -1.54   0.123    -4.405845    .5275972
                         e5 |   2.395286   1.471705     1.63   0.104    -.4892021    5.279775
                         z1 |   .0539494   .0330374     1.63   0.102    -.0108028    .1187017
                            |
               c.d2014#c.z1 |   .0205746   .0178223     1.15   0.248    -.0143564    .0555057
                            |
               c.d2015#c.z1 |   .0114224   .0205888     0.55   0.579     -.028931    .0517757
                            |
                  c.e4#c.z1 |   .1244352   .1057257     1.18   0.239    -.0827834    .3316538
                            |
                  c.e5#c.z1 |  -.1979284   .1326289    -1.49   0.136    -.4578764    .0620195
                            |
                      _cons |  -1.094794   .3960762    -2.76   0.006    -1.871089    -.318499
---------------------------------------------------------------------------------------------

. margins, dydx(treat) at(e4 = 1 e5 = 0 d2014 = 1 d2015 = 0) subpop(if e4)

Average marginal effects                        Number of obs     =      2,180
Model VCE    : Robust                           Subpop. no. obs   =        536

Expression   : Pr(ybin), predict()
dy/dx w.r.t. : 1.treat
at           : e4              =           1
               d2014           =           1
               d2015           =           0
               e5              =           0

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     1.treat |          .  (not estimable)
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.