The Kepler mission provides a wealth of multiple transiting planet systems ( MTPS ) .
The formation and evolution of multi-planet systems are likely to be influenced by companion stars given the abundance of multi stellar systems .
We study the influence of stellar companions by measuring the stellar multiplicity rate of MTPS .
We select 138 bright ( K _ { P } < 13.5 ) Kepler MTPS and search for stellar companions with AO imaging data and archival radial velocity ( RV ) data .
We obtain new AO images for 73 MTPS .
Other MTPS in the sample have archival AO imaging data from the Kepler Community Follow-up Observation Program ( CFOP ) .
From these imaging data , we detect 42 stellar companions around 35 host stars .
For stellar separation 1 AU < a < 100 AU , the stellar multiplicity rate is 5.2 \pm 5.0 % for MTPS , which is 2.8 \sigma lower than 21.1 \pm 2.8 % for the control sample , i.e. , the field stars in the solar neighborhood .
We identify two origins for the deficit of stellar companions within 100 AU to MTPS : ( 1 ) a suppressive planet formation , and ( 2 ) the disruption of orbital coplanarity due to stellar companions .
To distinguish between the two origins , we compare the stellar multiplicity rates of MTPS and single transiting planet systems ( STPS ) .
However , current data are not sufficient for this purpose .
For 100 AU < a < 2000 AU , the stellar multiplicity rates are comparable for MTPS ( 8.0 \pm 4.0 % ) , STPS ( 6.4 \pm 5.8 % ) , and the control sample ( 12.5 \pm 2.8 % ) .